Question

MNPQ is a rectangle. Find the measure of <1 and <2

Answer 1

Answer: ∠1 = 48°, ∠2 = 42°

Explanation:

• Because it's a rectangle, NP and MQ are parallel lines. ∠2 and (3x)° are alternate interior angles and are therefore equal.
• NM and PQ are also parallel lines. ∠1 is equal to (2x + 20)° because they're also alternate interior angles.

∠M = 90° = ∠1 + (3x)° = (2x + 20)° + (3x)°

2x + 20 + 3x = 90

2x + 3x = 90 - 20

5x = 70

x = 14

• Because ∠1 = (2x + 20)°,

∠1 = 2x + 20 = 2(14) + 20 = 28 + 20 = 48°

• Because ∠2 = (3x)°,

∠2 = 3x = 3(14) = 42°

(I hope this is right :\)