Question

The diagram below shows AABD with ray AC. BEI AD, andXEBD = *CBD. If mxABE = 52, what is m&D? (4 pts]

Answer 1

`m\angle D\text{ = }26`

Here, we want to calculate the measure of angle D

Firstly, we can calculate the measure of angle A

Since BE and AD are perpendicular, it follws that triangle ABE is a right angled triangle

Thus,

52 + A = 90

A = 90-52

A = 38

Now, from the question, we are told that EBD and CBD are congruent, meaning that they are equal

We can deduce from the diagarm that;

`\angle ABE\text{ + }\angle CBD\text{ + }\angle EBD\text{ = 180}`

The reason for this is that they are all on a straight line and the measure of angles on a straight line is 180

Thus, since we have the two angles equal, then;

`\begin{gathered} \angle EBD\text{ = }(180-52)/(2) \\ \\ \angle EBD\text{ = 64} \end{gathered}`

The measure of angle B in triangle ABD would be 64 + 52 = 116.

Since we have two angles out of triangle ABD, we can get the measure of the third angle which is angle D (Sum of angles in a triangle = 180)

Mathematically, that would be;

`\begin{gathered} \angle D\text{ + 116 + 38 = 180} \\ \angle D\text{ = 180-116-38} \\ \\ \angle D\text{ = 26} \end{gathered}`