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Answer:
(a) 84°
Step-by-step explanation:
If the upper side of angle 1 is extended so that it crosses the lower parallel, the angle it makes there corresponds to the one marked 51°, so is also 51°. That makes angle 1 the exterior angle of a triangle with remote interior angles of 51° and 33°. Angle 1 is the sum of those angles:
∠1 = 51° +33° = 84°
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Alternate solution
Draw a line through the vertex of angle 1 parallel to the other two parallel lines. The lower half of angle 1 is then an alternate interior angle to the one marked 33°, so is 33°. The upper half of angle 1 is a corresponding angle to the one marked 51°, so is 51°. That makes angle 1 be the sum of 33° and 51° angles, so 84°.
