Step-by-step explanation:
a. Given => <em>m</em>∠5 = 40°
b. Given => <em>m</em>∠2 = 140°
c. Same Side Interior Angle Theorem => The same side interior angles must add up to 180°, which in this case, it does. m∠4 and m∠2 are alternate interior angles, and so there measurements are the same. 180 - 140 = 40
d. Both angles are part of the "same-side interior angles", which means that there measurements should add up to 180°. Note that m∠5 = 40°, and m∠2 = 140° (Given). Set the equation
m∠5 + m∠2 = 180
Plug in the number for each angle
40 + 140 = 180
180 = 180 (True).
e. It is proven that the above measurements are congruent with their corresponding parts. This means that a || b through <em>Converse of Same Side Interior angle Theorem</em>.
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