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".
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