# ANGLE THEOREMS FOR TRIANGLES WORKSHEET

Angle Theorems for Triangles Worksheet :

Worksheet given in this section will be much useful for the students who would like to practice solving problems on triangles using angle theorems.

## Angle Theorems for Triangles Worksheet - Problems

Problem 1 :

Can 30°, 60° and 90° be the angles of a triangle ?

Problem 2 :

Can 35°, 55° and 95° be the angles of a triangle ?

Problem 3 :

In a triangle, if the second angle is 5° greater than the first angle and the third angle is 5° greater than second angle, find the three angles of the triangle.

Problem 4 :

Find m∠W and m∠X in the triangle given below. Problem 5 :

Find m∠A and m∠B in the triangle given below.  ## Angle Theorems for Triangles Worksheet - Solutions

Problem 1 :

Can 30°, 60° and 90° be the angles of a triangle ?

Solution :

Let us add all the three given angles and check whether the sum is equal to 180°.

30° +  60° + 90°  =  180°

Since the sum of the angles is equal 180°, the given three angles can be the angles of a triangle.

Problem 2 :

Can 35°, 55° and 95° be the angles of a triangle ?

Solution :

Let us add all the three given angles and check whether the sum is equal to 180°.

35° +  55° + 95°  =  185°

Since the sum of the angles is not equal 180°, the given three angles can not be the angles of a triangle.

Problem 3 :

In a triangle, if the second angle is 5° greater than the first angle and the third angle is 5° greater than second angle, find the three angles of the triangle.

Solution :

Let "x" be the first angle.

The second angle  =  x + 5

The third angle  =  x + 5 + 5  =  x + 10

We know that,

the sum of the three angles of a triangle  =  180°

x + (x+5) + (x+10)  =  180°

3x + 15  =  180

3x  =  165

x  =  55

The first angle  =  55°

The second angle  =  55 + 5  =  60°

The third angle  =  60 + 5  =  65°

Hence, the three angles of a triangle are 55°, 60° and 65°.

Problem 4 :

Find m∠W and m∠X in the triangle given below. Solution :

Step 1 :

Write the Exterior Angle Theorem as it applies to this triangle.

m∠W + m∠X  =  m∠WYZ

Step 2 :

Substitute the given angle measures.

(4y - 4)° + 3y°  =  52°

Step 3 :

Solve the equation for y.

(4y - 4)° + 3y°  =  52°

4y - 4 + 3y  =  52

Combine the like terms.

7y - 4  =  52

7y - 4 + 4  =  52 + 4

Simplify.

7y  =  56

Divide both sides by 7.

7y / 7  =  56 / 7

y  =  8

Step 4 :

Use the value of y to find m∠W and m∠X.

m∠W  =  4y - 4

m∠W  =  4(8) - 4

m∠W  =  28

m∠X  =  3y

m∠X  =  3(8)

m∠X  =  24

So, m∠W  =  28° and m∠X  =  24°.

Problem 5 :

Find m∠A and m∠B in the triangle given below. Solution :

Step 1 :

Write the Exterior Angle Theorem as it applies to this triangle.

m∠A + m∠B  =  m∠C

Step 2 :

Substitute the given angle measures.

(5y + 3)° + (4y + 8)°  =  146°

Step 3 :

Solve the equation for y.

(5y + 3)° + (4y + 8)°  =  146°

5y + 3 + 4y + 8  =  146

Combine the like terms.

9y + 11  =  146

Subtract 11 from both sides.

9y + 11 - 11  =  146 - 11

Simplify.

9y  =  135

Divide both sides by 9.

9y / 9  =  135 / 9

y  =  15

Step 4 :

Use the value of y to find m∠A and m∠B.

m∠A  =  5y + 3

m∠A  =  5(15) + 3

m∠A  =  75 + 3

m∠A  =  78

m∠B  =  4y + 8

m∠B  =  4(15) + 8

m∠B  =  60 + 8

m∠B  =  68

So, m∠A  =  78° and m∠B  =  68°. After having gone through the stuff given above, we hope that the students would have understood how to solve problems on triangles using angle theorems.

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