Question

How do I get to the answer of this question?

Answer 1

(A) 45 degrees

Step-by-step explanation:

Given that triangle BCD is an Isosceles Triangle where BD=CD.

• Then the base angles of Isosceles triangle BCD: ,Angles B and C are congruent and are both 50 degrees.

The sum of the angles in a triangle is 180 degrees, therefore, in triangle BCD:

`\begin{gathered} m\angle B+m\angle C+m\angle D=180\degree \\ 50\degree+50\degree+m\angle D=180\degree \\ m\angle D=180\degree-100\degree \\ m\angle D=80\degree \end{gathered}`

As can be seen in the diagram below:

Angle D (in triangle BDC) is an exterior angle of opposite interior angles A and B (in triangle BAD).

The sum of opposite interior angles is equal to the exterior angle.

`\begin{gathered} m\angle A+m\angle B=m\angle D \\ m\angle A+35\degree=80\degree \\ \text{Subtract 35 from both sides} \\ m\angle A=80\degree-35\degree \\ m\angle A=45\degree \end{gathered}`

The measure of angle A is 45 degrees.