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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

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 class=

Sagot :

Answer:

The correct option is OPTION C.

Step-by-step 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.

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