﻿ Missing Angles in Triangles Worksheet | Problems & Solutions

# Missing Angles in Triangles Worksheet

Missing Angles in Triangles Worksheet
• Page 1
1.
Find the value of $x$ in the figure.

 a. 30o b. 45o c. 50o d. 60o

#### Solution:

In the figure, all the sides of the triangle are equal.

So, the triangle is an equilateral triangle.

In an equilateral triangle, the measure of each angle is equal to 60o.

So, the measure of x is 60°.

2.
Find the measure of $x$.

 a. 90° b. 60° c. 180° d. 120°

#### Solution:

The sum of the measures of all the three angles of a triangle is 180.

The sum of the measures of the three angles in the figure is 30° + 60° + x.

30° + 60° + x = 180°
[Equate the sum of the measures of the three angles of the triangle to 180°.]

90° + x = 180°

x = 90°
[Subtract 90 from each side.]

3.
Find the measure of the third angle.

 a. 90° b. 120° c. 100° d. 110°

#### Solution:

The sum of all the angle measures of a triangle is 180°.

In the triangle, the sum of all the 3 angle measures is 30° + 40° + X.

30° + 40° + X = 180°
[Equate the sum of all the three angle measures of the triangle to 180°.]

70° + X = 180°

X = 110°
[Subtract 70° from both sides.]

So, the measure of the third angle of the triangle is 110°.

4.
The measures of two angles of a triangle are 80° and 50°. Find the measure of the third angle.
 a. 70° b. 50° c. 60° d. 40°

#### Solution:

The sum of all the angle measures of a triangle is 180°.

Let x be the measure of the third angle.

80° + 50° + x = 180°
[Equate the sum of all the angle measures of the triangle to 180°.]

130° + x = 180°

x = 50°
[Subtract 130° from both the sides.]

5.
What is the value of $x$ in the figure?

 a. 60° b. 90° c. 80° d. 70°

#### Solution:

The sum of all the angle measures of a triangle is 180o.

60° + 50° + x = 180°
[Equate the sum of angles of the triangle to 180°.]

110° + x = 180°

x = 70°
[Subtract 110° from each side.]

6.
Two angles in a triangle measure 30° and 14°. Find the measure of the third angle.
 a. 316° b. 166° c. cannot be determined. d. 136°

#### Solution:

The sum of the measures of all the three angles in a triangle is 180° .

The measure of the third angle = 180 - (30 + 14)
[Given, two angles measure 30° and 14° .]

180 - (30 + 14) = 180 - 44 = 136
[Simplify.]

The measure of the third angle in the triangle is 136° .

7.
Find the sum of angle $x$° and angle $y$° in the right triangle.

 a. 90° b. 270° c. 120° d. 180°

#### Solution:

The sum of all the angle measures of a triangle is 180°.

The angles are x°, y°, and 90°.

x° + y° + 90° = 180°
[Equate the sum of angles of the triangle to 180°.]

x° + y° = 90°
[Subtract 90° from each side.]

The sum of angle x° and angle y° from the right triangle is 90°.

8.
The triangle shown here is a right isosceles triangle. Find the values of $x$ and $y$.

 a. 60° and 60° b. 45° and 45° c. 60° and 45° d. 45° and 60°

#### Solution:

The sum of three angles in a triangle is equal to 180°.

The triangle is a right isosceles triangle. So x = y.

90° + x + y = 180°
[Sum of the angles in a triangle.]

90° + y + y = 180°
[Substitute x = y.]

90° + 2 y = 180°

2y = 180° - 90° = 90°
[Subtract 90° from each side.]

y = 90° / 2= 45°
[Divide each side by 2.]

x = y = 45°

9.
Find the value of $x$ in the figure.

 a. 30° b. 60° c. 45° d. 15°

#### Solution:

In a triangle, sum of all the angles is 180°.

So, 90° + 60° + x° = 180° .

x° = 30°
[Simplify.]

So, the value of x is 30°.

10.
Two angles of a triangle measure 60° and 50°. Find the measure of the third angle.
 a. 65° b. 80° c. 70° d. 75°

#### Solution:

The sum of the measures of angles in a triangle is 180°.

The measure of the third angle = 180° - (60° + 50°).

= 70°

So the measure of the third angle is 70°.