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

Option A. 52°

Explanation:

From the figure attached,

JEFH is a parallelogram and ΔFGH is a scalene right triangle.

If m∠JEF = 142°

m∠JHF = 142° [Since opposite angles of the parallelogram are equal]

m∠FHG + m∠JHF = 180°

m∠FHG + 142° = 180°

m∠FHG = 180 - 142

= 38°

In the given scalene right triangle FGH,

m∠FHG + m∠HFG + m∠HGF = 180°

38° + m∠HFG + 90° = 180°

m∠HFG = 180° - 128°

m∠HFG = 52°

Option A. will be the answer.