Answer:
∠1 = 40°
∠2 = 23°
∠3 = 35°
∠4 = 82°
Step-by-step explanation:
The points where segments intersect the sides of triangle GHJ can be named as follows: P on GH, Q on HJ, R on JG.
Segments PQ and JG are parallel, which makes it possible to identify these relations:
∠2 ≅ 23° . . . . . alternate interior angles at transversal GQ
∠4 +23° = 105° ⇒ ∠4 = 82° . . . . alt interior angles at transversal RQ
The fact that acute angles in a right triangle are complementary can be used to find angle 3.
∠3 = 90° -55° = 35°
All of the angles at Q total a linear angle, so we have ...
∠1 +∠4 +23° +∠3 = 180°
∠1 = 180° -82° -23° -35° = 40°
