# ANGLE PAIRS AND TWO STEP EQUATIONS WORKSHEET

Problem 1 :

Find the measure of EHF.

Problem 2 :

Find the measure of ∠ZXY.

Problem 3 :

Find the measure of ∠JML.

Problem 1 :

Find the measure of mEHF.

Step 1 :

Identify the relationship between mEHF and mFHG.

Since angles mEHF and mFHG form a straight line, the sum of the measures of the angles is 180°.

m∠EHF and mFHG 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 + mFHG  =  180°

2x + 48° = 180°

Subtract 48° from each side.

2x  =  132°

Divide each side by 2.

x  =  66°

Step 3 :

Find the measure of mEHF.

m∠EHF  =  2x

m∠EHF  =  2(66°)

m∠EHF  =  132°

So, the measure of mEHF is 132°.

Problem 2 :

Find the measure of m∠ZXY.

Step 1 :

Identify the relationship between mWXZ and mZXY.

m∠WXZ and mZXY are complementary angles.

Step 2 :

Write and solve an equation to find x.

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

m∠WXZ + mZXY  =  90°

4x + 7° + 35° = 90°

4x + 42°  =  90°

Subtract 42° from each side.

4x  =  48°

Divide each side by 4.

x  =  12°

Step 3 :

Find the measure of mEHF.

m∠ZXY  =  4x + 7°

m∠ZXY  =  4(12°) + 7°

m∠ZXY  =  48° + 7°

m∠ZXY  =  55°

So, the measure of mZXY is 55°.

Problem 3 :

Find the measure of m∠JML.

Step 1 :

Identify the relationship between mJML and mLMN.

Since angles mJML and mLMN form a straight line, the sum of the measures of the angles is 180°.

m∠JML and mLMN are supplementary angles.

Step 2 :

Write and solve an equation to find x.

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

m∠JML + mLMN  =  180°

3x + 54° = 180°

Subtract 54° from each side.

3x  =  126°

Divide each side by 3.

x  =  42°

Step 3 :

Find the measure of m∠JML.

m∠JML  =  3x

m∠JML  =  3(42°)

m∠JML  =  126°

So, the measure of mJML is 126°.

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