Answer: x = 40
Explanation:
3x + x + 20 = 180 same side (consecutive) interior angles
4x + 20 = 180
4x = 160
x = 40
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Answer: x = 24
Explanation:
6x - 24 + 2x + 12 = 180 linear pair (supplementary angles)
8x - 12 = 180
8x = 192
x = 24
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Answer: x = 16
Explanation:
base angles of an isosceles triangle are congruent
2(2x + 15) + 6x - 10 = 180 triangle sum theorem
4x + 30 + 6x - 10 = 180
10x + 20 = 180
10x = 160
x = 16
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Let ∠1 and ∠2 represent the exterior angles in the diagram and "x" represent the same side (consecutive) interior angle with ∠1.
Then m∠1 + x = 180 same side interior angle theorem
and m∠2 + x = 180 linear pairs are supplementary
m∠1 + x = m∠2 + x transitive property
m∠1 = m∠2 subtraction property of equality
∠1 ≈ ∠2 definition of congruency