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

In the given rhombus 𝐴𝐡𝐢𝐷, π‘šβˆ π΅πΆπ· = 36Β°. Find π‘šβˆ π΅π΄πΆ.

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Video Transcript

In the given rhombus 𝐴𝐡𝐢𝐷, the measure of angle 𝐡𝐢𝐷 equals 36 degrees. Find the measure of angle 𝐡𝐴𝐢.

Let’s recall that a rhombus is a quadrilateral or four-sided shape that has all four sides equal in length. We’re told that the angle 𝐡𝐢𝐷 is 36 degrees. We need to find this smaller angle 𝐡𝐴𝐢. In order to do this, we’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 𝐡𝐴𝐷 would be equal to angle 𝐡𝐢𝐷. They’ll both be 36 degrees. Of course, the angle that we’re looking for is angle 𝐡𝐴𝐢. Now, while it might look as though it’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 𝐴𝐢 is a diagonal of the rhombus.

We can note down what we’ve discovered. Angle 𝐡𝐴𝐷 is equal to angle 𝐡𝐢𝐷 because they’re opposite angles. And we’ve determined that both of those will then be 36 degrees. Angle 𝐡𝐴𝐢 will be half of angle 𝐡𝐴𝐷 because we have the diagonals bisecting the angles. To find the measure of angle 𝐡𝐴𝐢, we’ll half 36 degrees, giving us an answer of 18 degrees.

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