Applying the same-side interior angles theorem,
7. m∠4 = 50°; m∠5 = 130°
8. m∠2 = 15°; m∠8 = 15°.
<h3>What is the Same-Side Interior Angles Theorem?</h3>
The same-side interior angles theorem holds that, two interior angles on a side of a transversal are supplementary, that is they add up to 180 degrees.
<h3>What is the
Alternate Exterior Angles Theorem?</h3>
According to the alternate exterior angles theorem, exterior angles that alternate each other along a transversal are congruent, that is they have equal measures.
7. m∠4 + m∠5 = 180 [same-side interior angles theorem]
Substitute
y + 2y + 30 = 180
3y + 30 = 180
3y = 180 - 30
3y = 150
y = 50
m∠4 = y = 50°
m∠5 = 2y + 30 = 2(50) + 30
m∠5 = 130°
8. m∠2 = m∠8 [alternate exterior angles theorem]
Substitute
x - 30 = 3x - 120
x - 3x = 30 - 120
-2x = -90
x = 45
m∠2 = x - 30 = 45 - 30 = 15°
m∠8 = 3x - 120 = 3(45) - 120 = 15°
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