Triangle Angles 2 Sample Problems

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Triangle Angles 2

To review the basics of triangle angles, see here.

In this topic, you will need to understand supplementary angles. Two angles are supplementary angles if the sum of their angles is 180^o. Angles on a straight line always add up to 180^o.

This example shows angles on a straight line.
The angles 65^o and 115^o are supplementary angles because their angles add up to 180^o.

Example 1: Supplementary angles

Find the value of 'x'. Diagrams are not always to scale.
x =
The angles that measure 2x and 18x lie on a straight line so they are supplementary angles.
This means that 2x + 18x = 180.

2x + 18x = 180

20x = 180

20x ÷ 20 = 180 ÷ 20

x = 9

Example 2: Triangle angles

Find the value of 'x'. Diagrams are not always to scale.
x =
The angle next to the 79^o angle and the 79^o angle are angles on a straight line so they are supplementary angles.

angle next to 79^o + 79^o = 180^o

angle next to 79^o = 180^o - 79^o

Since the angles of a triangle add up to 180^o, we know that

x^o + 34^o + angle next to 79^o angle = 180^o

x + 34 + (180 - 79) = 180

x + 34 + 101 = 180

x + 135 = 180

x = 45

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angle next to 79^o + 79^o	=	180^o
angle next to 79^o	=	180^o - 79^o

x^o + 34^o + angle next to 79^o angle	=	180^o
x + 34 + (180 - 79)	=	180
x + 34 + 101	=	180
x + 135	=	180
x	=	45