# SUM OF ANGLE MEASURES IN A TRIANGLE WORKSHEET

## About "Sum of angle measures in a triangle worksheet"

Sum of angle measures in a triangle worksheet :

Worksheet given in this section is much useful to the students who would like to practice problems on "Triangle sum theorem".

## Sum of angle measures in a triangle worksheet - Problems

1. Can a triangle have two right angles ? Explain.

2. Describe the relationship between the two acute angles in a right triangle. Explain your reasoning.

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

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

5. 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.

## Sum of angle measures in a triangle worksheet - Solution

Problem 1 :

Can a triangle have two right angles ? Explain.

Solution :

No

The sum of the measures of two right angles is 180°. That means the measure of the third angle would be

180° - 180°  =  0°

which is impossible.

Problem 2 :

Describe the relationship between the two acute angles in a right triangle. Explain your reasoning.

Solution :

No

They are complementary.

The sum of their measures must be

180° - (measure of the right angle)  =  180° - 90°  =  90°

Problem 3 :

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 4 :

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 5 :

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°.

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