# ANGLE PAIRS AND TWO STEP EQUATIONS

## About "Angle pairs and two step equations"

Angle pairs and two step equations :

Vertical angles are the opposite angles formed by two intersecting lines. Vertical angles are congruent because the angles have the same measure.

Adjacent angles are pairs of angles that share a vertex and one side but do not overlap.

Complementary angles are two angles whose measures have a sum of 90°.

Supplementary angles are two angles whose measures have a sum of 180°. We discovered in the Explore Activity that adjacent angles formed by two intersecting lines are supplementary.

## Angle pairs and two step equations - Examples

Example 1 :

Find the measure of angle <EHF. Step 1 :

Identify the relationship between <EHF and <FHG.

Since angles <EHF and <FHG form a straight line, the sum of the measures of the angles is 180°.

<EHF and <FHG are supplementary angles.

Step 2 :

Write and solve an equation to find x.

The sum of the measures of supplementary angles is 180°.

m<EHF + m<FHG  =  180°

2x + 48° = 180°

Subtract 48° from both sides.

(2x + 48°) - 48°  =  180° - 48°

2x  =  132°

Divide both sides by 2.

(2x) / 2  =  (132°) / 2

x  =  66°

Step 3 :

Find the measure of <EHF.

m<EHF  =  2x

m<EHF  =  2(66°)

m<EHF  =  132°

Hence, the measure of <EHF is 132°

Example 2 :

Find the measure of angle <ZXY. Step 1 :

Identify the relationship between <WXZ and <ZXY.

<WXZ and <ZXY are supplementary angles.

Step 2 :

Write and solve an equation to find x.

The sum of the measures of complementary angles is 90°.

m<WXZ + m<ZXY  =  90°

4x + 7° + 35° = 90°

4x + 42°  =  90°

Subtract 42° from both sides.

(4x + 42°) - 42°  =  90° - 42°

4x  =  48°

Divide both sides by 4.

(4x) / 4  =  (48°) / 4

x  =  12°

Step 3 :

Find the measure of <EHF.

m<ZXY  =  4x + 7°

m<ZXY  =  4(12°) + 7°

m<ZXY  =  48° + 7°

m<ZXY  =  55°

Hence, the measure of <ZXY is 55°

After having gone through the stuff given above, we hope that the students would have understood "One step equations on angle pairs".