ANGLE THEOREMS FOR TRIANGLES WORKSHEET

About "Angle theorems for triangles worksheet"

Angle theorems for triangles worksheet :

Worksheet given in this section is much useful to the students who would like to practice problems on triangle sum theorem and exterior angle theorem in triangles. 

Angle theorems for triangles worksheet - Problems

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

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

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. 

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

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

Angle theorems for triangles worksheet - Solution

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

Add 4 to both sides.

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 "Angle theorems for triangles worksheet". 

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