If you are interested in learning more about other angle topics, you can enter one of the following articles:
- Angle Notation
- Sides, Vertices, and Angles
- Bisector
- Acute Angle
- Obtuse Angle
- Plane Angle
- Adjacent Angles
- Vertically Opposite Angles
- Alternate Angles
- Corresponding Angles
- Sum of the Angles of a Triangle
- Sum of the Angles of a Polygon
- Sum and Difference of Angles
In the Mathematics Blog of Tutorela you will find a wide variety of articles about mathematics
Several Examples of Right Angles
Right angles within a circle
Right angles within a triangle
Right angles within a square
Right angles within a rectangle
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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?
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°
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?
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?
Exercise 3
Given the triangle △ABC:
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.
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
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
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
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
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?
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?