Question

Use the figure below to solve for the measurement of the numbered angle

Given s || t and l || m
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Answer 1

∠ 6 = 100°

Explanation:

∠ 1 and ∠ 2 are a linear pair and sum to 180° , that is

∠ 1 + ∠ 2 = 180

x + 20 + x = 180

2x + 20 = 180 ( subtract 20 from both sides )

2x = 160 ( divide both sides by 2 )

x = 80

then

∠ 1 = x + 20 = 80 + 20 = 100°

∠ 1 and ∠ 6 are vertically opposite angles and are congruent , so

∠ 6 = 100°