Question

A

B
E
D
С
Note: Figure is not drawn to scale.
In rhombus ABCD, segments AC and BD are diagonals. If mZDAB = 160°, what is the measure of ZABE?
OA. 190°
ОВ.
170°
OC
10°
D.
100

Answer 1

The correct option is OPTION C.

Explanation:

Recall that for a rhombus, the diagonals bisect the interior angles.

This means that if we are given that:

m∠DAB=160°

Then:

m∠EAB=m∠DAB/2=160/2=80°

Also, recall that the diagonals of a rhombus are perpendicular. Therefore:

m∠AEB=90°

Hence, we can have a triangle that looks like the one shown below:

Recall that the sum of angles in a triangle is 180°. Therefore, we have that:

m∠AEB+m∠ABE+m∠EAB=180°

Hence, we can calculate m∠ABE to be:

m∠ABE =180-80-90

m∠ABE=10°

The correct option is OPTION C.