**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.

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.

**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°.

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