Question

In the figure below, quadrilateral EFHJ is a parallelogram, and triangle FGH is a scalene right triangle.

Note: picture not drawn to scale

If mJEF = 142°, what is mHFG?
A.
52°
B.
60°
C.
30°
D.
38°

Answer 1

A

Explanation:

In a parallelogram the opposite angles are congruent, thus

∠ JHF = ∠ JEF = 142°

∠ JHF and ∠ FHG are adjacent angles and are supplementary, thus

∠ FHG = 180° - 142° = 38°

The sum of the 3 angles in a triangle = 180° , thus

∠ HFG = 180° - (90 + 38)° = 180° - 128° = 52° → A