Answer:
(A) 45 degrees
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:
[tex]\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}[/tex]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.
[tex]\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}[/tex]
The measure of angle A is 45 degrees.
