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Several Examples of Right Angles
Right angles within a circle
![A3 - Right angles within a circle](/_ipx/f_png,s_500x471/https://cdn.tutorela.com/images/A3_-_Right_angles_within_a_circle.width-500.png)
Right angles within a triangle
![Right angles within a triangle](/_ipx/f_png,s_500x431/https://cdn.tutorela.com/images/Angulos_rectos_dentro_de_un_triangulo.width-500.png)
Right angles within a square
![A5 - Right angles within a square](/_ipx/f_png,s_500x494/https://cdn.tutorela.com/images/A5_-_Right_angles_within_a_square.width-500.png)
Right angles within a rectangle
![A6 - Right angles within a rectangle](/_ipx/f_png,s_500x355/https://cdn.tutorela.com/images/A6_-__Right_angles_within_a_rectangle.width-500.png)
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Exercise
Exercise 1
How many degrees do we need to add to angle β so that there is another parallel line in the following graph?
![Exercise 3 on parallel lines](/_ipx/f_png,s_500x350/https://cdn.tutorela.com/images/Ejercicio_3_sobre_rectas_paralelas.width-500.png)
Explanation
By adding 4° degrees to the angle ∡β we get an angle of 90º degrees and basically another parallel line will be created below the two of them.
86°+4°=90°
![Exercise 4 on parallel lines solution](/_ipx/f_png,s_500x305/https://cdn.tutorela.com/images/Ejercicio_4_sobre_rectas_paralelas_solucion.width-500.png)
Solution:
The correct answer is: 4º
Exercise 5 (on parallel lines)
This question is divided into several parts:
- How many degrees is the angle of ∡ABC and what type of angle is it in relation to ∡CBF?
- How many degrees is the angle ∡BDE and what type of angle is it in relation to ∡ADC?
![Exercise 5 on parallel lines](/_ipx/f_png,s_500x552/https://cdn.tutorela.com/images/Ejercicio_5_sobre_rectas_paralelas.width-500.png)
Answer 1:
A. The angle of ∡ABC is equal to 180º−130º=50º
B. The angle of ∡ABC in relation to the angle of ∡CBF is called Adjacent angles
Answer 2:
- The angle ∡BDE is equal to 90º since it is a vertex opposite angle in relation to the angle ∡ADC=90º
Do you know what the answer is?
Question 1 Exercise 3
Given the triangle △ABC:
![Exercise 2 Given the triangle ABC](/_ipx/f_png,s_500x608/https://cdn.tutorela.com/images/Ejercicio_2__Dado_el_triangulo_ABC.width-500.png)
Task:
Find the length of BC
Solution:
Pythagorean Theorem - Apply the formula
Given the triangle △ABC in the drawing.
Assignment:
Find the length of BC
Solution:
Write the Pythagorean Theorem for the right triangle △ABC
AB2+BC2=AC2
We place the known lengths:
52+BC2=132
25+BC2=169
BC2=169−25=144,
BC=12
Answer:
12 cm.
Exercise 4
Homework:
In front of you is a right triangle, calculate its area.
![a right triangle, calculate its area](/_ipx/f_png,s_500x389/https://cdn.tutorela.com/images/un_triangulo_rectangulo_calcular_su_area.width-500.png)
Solution:
Calculate the area of the triangle using the formula for calculating the area of a right triangle.
2leg×leg
2AB⋅BC=28⋅6=248=24
Answer:
The answer is 24 cm².
Exercise 5
Homework:
Given the right triangle △ADB
The perimeter of the triangle is equal to 30 cm.
Given:
AB=15
AC=13
DC=5
CB=4
Calculate the area of the triangle △ABC
![Given the right triangle ADB](/_ipx/f_png,s_500x599/https://cdn.tutorela.com/images/Dado_el_triangulo_rectangulo_ADB.width-500.png)
Solution:
Given the perimeter of the triangle △ADC equal to 30 cm.
From here we can calculate AD.
AD+DC+AD=PerimeterΔADC
AD+5+13=30
AD+18=30 /−18
AD=12
Now we can calculate the area of the triangle ΔABC
Pay attention: we are talking about an obtuse triangle therefore its height is AD.
We use the formula to calculate the area of the triangle:
2sideheight×side=
2AD⋅BC=212⋅4=248=24
Answer:
The area of the triangle ΔABC is equal to 24 cm².
Exercise 6
Homework:
Given the right triangle ΔABC
The area of the triangle is equal to 38 cm², AC=8
Find the measure of the leg BC
![5.a The area of the triangle is equal to 38 cm²](/_ipx/f_png,s_500x486/https://cdn.tutorela.com/images/5.a_El_area_del_triangulo_es_igual_a_38.width-500.png)
Solution:
We will calculate the length of BC using the formula for calculating the area of a right triangle:
2leg×leg
2AC⋅BC=28⋅BC=38
Multiply the equation by the common denominator
/ ×2
Then divide the equation by the coefficient of BC
8×BC=76 /:8
BC=9.5
Answer:
The length of the leg BC is equal to 9.5 centimeters.
Do you think you will be able to solve it?
Exercise 7
![Exercise 4 In front of you, there is a right triangle ABC](/_ipx/f_png,s_500x499/https://cdn.tutorela.com/images/Ejercicio_4__Frente_a_usted_hay_un_triangulo_r.width-500.png)
In front of you, there is a right triangle ΔABC.
Given that BC=6 The length of the leg AB is greater by 3331% than the length of BD.
The area of the triangle ΔADC is greater by 25 than the area of the triangle ΔABD.
Task:
What is the area of the triangle ΔABC?
Solution:
To find the measure of the leg AB we will use the data that its length is greater by 33.33 than the length of BD.
AB=1.33333⋅BD
(100100+10033.33=100133.33=1.333)
AB=1.333⋅6=8
Now we will calculate the area of the triangle ΔABD.
SΔABD=2AB⋅BD=28⋅6=248=24
Answer:
24 cm².
Exercise 8
![the area of the triangle is 24 cm²](/_ipx/f_png,s_500x499/https://cdn.tutorela.com/images/el_area_del_triangulo_sea_de_24_cm2.width-500.png)
Homework:
What data in the graph is incorrect?
For the area of the triangle to be 24 cm², what is the data that should replace the error?
Solution:
Explanation: area of the right triangle.
SΔEDF=2ED⋅EF=28⋅6=248=24
According to the formula:
2leg×leg
If the area of the triangle can also be calculated from the formula of:
2side×heightofside
2EG×10=24 /×2
10EG=48 /:10
EG=4.8
Answer:
The incorrect data is EG.
The length of EG should be 4.8 cm.
Exercise 9
In the following example, a square ABCD is presented.
A. Is the angle ∡ABC equal to the angle of ∡ADC? Can it be said that BD serves as the bisector of the angle ∡ABC?
Bisector inside a square
![A -Bisector inside a square](/_ipx/f_png,s_500x452/https://cdn.tutorela.com/images/A_-Bisector_inside_a_square.width-500.png)
Solution to exercise 2:
The line BD created 2 points where the angle was divided into 2 equal angles.
Answer:
Therefore, DB is a bisector of the two angles ∡ADC and ∡ABC
Do you know what the answer is?
examples with solutions for right angle
Exercise #1
True or false?
One of the angles in a rectangle may be an acute angle.
Video Solution
Step-by-Step Solution
One of the properties of a rectangle is that all its angles are right angles.
Therefore, it is not possible for an angle to be acute, that is, less than 90 degrees.
Answer
Exercise #2
If the two adjacent angles are not equal to each other, then one of them is obtuse and the other acute.
Video Solution
Answer
Exercise #3
Which figure depicts a right angle?
Video Solution
Answer
Exercise #4
Which of the following angles are obtuse?
Video Solution
Answer
Exercise #5
Choose the appropriate triangle according to the following:
Angle B equals 90 degrees.
Video Solution
Answer