Question Video: Finding the Measure of an Angle Using the Properties of a Rhombus | Nagwa Question Video: Finding the Measure of an Angle Using the Properties of a Rhombus | Nagwa

# Question Video: Finding the Measure of an Angle Using the Properties of a Rhombus

In the given rhombus π΄π΅πΆπ·, πβ π΅πΆπ· = 36Β°. Find πβ π΅π΄πΆ.

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### Video Transcript

In the given rhombus π΄π΅πΆπ·, the measure of angle π΅πΆπ· equals 36 degrees. Find the measure of angle π΅π΄πΆ.

Letβs recall that a rhombus is a quadrilateral or four-sided shape that has all four sides equal in length. Weβre told that the angle π΅πΆπ· is 36 degrees. We need to find this smaller angle π΅π΄πΆ. In order to do this, weβll need to remember some of the properties of a rhombus.

One of the angle properties is that opposite angles are equal. Looking at the diagram, this would mean that angle π΅π΄π· would be equal to angle π΅πΆπ·. Theyβll both be 36 degrees. Of course, the angle that weβre looking for is angle π΅π΄πΆ. Now, while it might look as though itβs half of this angle, we need to be sure. We can in fact recall that the diagonals will bisect the angles, which means they cut them exactly in half. Line segment π΄πΆ is a diagonal of the rhombus.

We can note down what weβve discovered. Angle π΅π΄π· is equal to angle π΅πΆπ· because theyβre opposite angles. And weβve determined that both of those will then be 36 degrees. Angle π΅π΄πΆ will be half of angle π΅π΄π· because we have the diagonals bisecting the angles. To find the measure of angle π΅π΄πΆ, weβll half 36 degrees, giving us an answer of 18 degrees.

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