Question

Find the value of the angle, ∠XAB, in the rhombus ABCD.

• A. ${50}^o$
• B. ${55}^o$
• C. ${45}^o$
• D. ${45}^o$

Answer 1

The correct option is A ${50}^o$

DXB is the diagonal that bisects ∠ABC.
Since ∠ABX = 40 °, ∠ABC = 2 × 40 = 80°
Now, in a rhombus, the sum of adjacent angles is 180°.
So, ∠ABC +∠BAD = 180°
80° + ∠BAD = 180°
∠BAD= 180 – 80=100°
∠BAD = 100°
∠BAD is bisected by diagonal AXC.
So, ∠ XAB = 50 °