Question

In the figure, angle A measures 45° and angle E measures 15°.

Answer 1

Answer:

∠C = 45°   ∠D = 30°

Step-by-step explanation:

Given in the figure attached.

∠A = 45° and ∠E = 15°

We have to find the measures of ∠C and ∠D.

(A) Since ∠A + ∠B + ∠C = 180°

                45° + 90° + ∠C = 180°

               135 + ∠C = 180°

                        ∠C = 180 - 135 = 45°

(B) Now ∠C + ∠F = 180° ( supplementary angles )

             45 + ∠F = 180

                      ∠F = 180 - 45

                             = 135°

Since ∠D +∠E + ∠F = 180°

          ∠D + 15 + 135 = 180

                 ∠D + 150 = 180

                           ∠D = 180 - 150

                                 = 30°

Therefore, ∠C = 45°

                  ∠D = 30°

Answer 2

Answer:

Angle C = 45 degrees.

Angle D = 30 degrees.  

Step-by-step explanation:

Angle C = 45 + 90 = 135   180 - 135 = 45.

Angle D = 180 - 45 = 135 (angle F)   15 + 135 = 150   180 - 150 = 30