Question

1. the diagonals of rhombus defg intersect at h. given that m∠egf = 20°, find the m∠efg.

Explanation:

Step1: Recall rhombus properties

Diagonals bisect angles and are perpendicular.

Step2: Analyze triangle GHF

$\triangle GHF$ is right-angled at $H$, $\angle EGF=20^\circ$.

Step3: Calculate $\angle GFH$

$\angle GFH = 90^\circ - 20^\circ = 70^\circ$.

Step4: Find $\angle EFG$

Diagonal $EG$ bisects $\angle EFG$, so $\angle EFG=2\times70^\circ=140^\circ$.

Answer:

140°