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Question

asked Oct 10, 2022 169k views

1 Answer

Pavel Chernikov · Answer 1 · 2022-10-15T13:37:47+0000

Given:

The figure of a rhombus.

To find:

The measure of angle 1.

Solution:

First label the vertices of the rhombus as shown in the below figure.

We know that the opposite angles of a rhombus are congruent and the diagonals of a rhombus bisect each vertex angle.

$m\angle ABD=m\angle CBD=30^\circ$ (Diagonal BD is the angle bisector)

Now,

$m\angle ABC=m\angle ABD+m\angle CBD$

$m\angle ABC=30^\circ+30^\circ$

$m\angle ABC=60^\circ$

We know that the consecutive angles of a rhombus are supplementary. It means the sum of each pair of consecutive angles is 180 degrees.

$m\angle BAD+m\angle ABC=180^\circ$

$m\angle 1+60^\circ=180^\circ$

$m\angle 1=180^\circ-60^\circ$

$m\angle 1=120^\circ$

Therefore, the measure of angle 1 is
$m\angle 1=120^\circ$ .