**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.

**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".

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