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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 $\triangle ABC$ :

Task:

Find the length of $BC$

Solution:

Pythagorean Theorem - Apply the formula

Given the triangle $\triangle ABC$ in the drawing.

Assignment:

Find the length of $BC$

Solution:

Write the Pythagorean Theorem for the right triangle $\triangle ABC$

$AB²+BC²=AC²$

We place the known lengths:

$5²+BC²=13²$

$25+BC²=169$

$BC²=169-25=144$ ,$\sqrt{}$

$BC=12$

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 .

$\frac{leg\times leg}{2}$

$\frac{AB\cdot BC}{2}=\frac{8\cdot6}{2}=\frac{48}{2}=24$

Answer:

The answer is $24$ cm².

Exercise 5 Homework:

Given the right triangle $\triangle ADB$

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 $\triangle ABC$

Solution:

Given the perimeter of the triangle $\triangle ADC$ 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:

$\frac{sideheight\times side}{2}=$

$\frac{AD\cdot BC}{2}=\frac{12\cdot4}{2}=\frac{48}{2}=24$

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:

$\frac{leg\times leg}{2}$

$\frac{AC\cdot BC}{2}=\frac{8\cdot BC}{2}=38$

Multiply the equation by the common denominator

/ $\times2$

Then divide the equation by the coefficient of $BC$

$8\times BC=76$ /$:8$

$BC=9.5$

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 $33\frac{1}{3}\%$ 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 $BD$ .

$AB=1.33333\cdot BD$

$(\frac{100}{100}+\frac{33.33}{100}=\frac{133.33}{100}=1.333)$

$AB=1.333\cdot6=8$

Now we will calculate the area of the triangle ΔABD.

$SΔ\text{ABD}=\frac{AB\cdot BD}{2}=\frac{8\cdot6}{2}=\frac{48}{2}=24$

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.

$SΔEDF=\frac{ED\cdot EF}{2}=\frac{8\cdot6}{2}=\frac{48}{2}=24$

According to the formula:

$\frac{leg\times leg}{2}$

If the area of the triangle can also be calculated from the formula of:

$\frac{side\times heightofside}{2}$

$\frac{EG\times10}{2}=24$ /$\times2$

$10EG=48$ /$:10$

$EG=4.8$

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

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 True or false?

An acute angle is smaller than a right angle.

Step-by-Step Solution The definition of an acute angle is an angle that is smaller than 90 degrees.

Since an angle that equals 90 degrees is a right angle, the answer is correct.

Answer Exercise #3 If the two adjacent angles are not equal to each other, then one of them is obtuse and the other acute.

Video Solution Step-by-Step Solution The answer is correct because the sum of two acute angles will be less than 180 degrees and the sum of two obtuse angles will be greater than 180 degrees

Answer Exercise #4 Which figure depicts a right angle?

Video Solution Step-by-Step Solution A right angle is equal to 90 degrees. In diagrams A+C, we see that the angle symbol is a symbol representing an angle that equals 90 degrees.

Answer Exercise #5 Choose the appropriate triangle according to the following:

Angle B equals 90 degrees.

Video Solution Step-by-Step Solution Let's note in which of the triangles angle B forms a right angle, meaning an angle of 90 degrees.

In answers C+D, we can see that angle B is smaller than 90 degrees.

In answer A, it is equal to 90 degrees.

Answer