Question

Quadrilateral ABCD is a parallelogram. What is the measure of ∠DAB? Show your work.

Answer 1

Answer:

∠ DAB = 133°

Step-by-step explanation:

In a parallelogram ABCD, the opposite angles are equal. That means ∠ A = ∠ C and ∠ B = ∠ D.

Now, it is given that ∠ D = 3x + 17 and ∠ B = 5x - 3

So, 3x + 17 = 5x - 3

⇒ 2x = 20  

⇒ x = 10

Therefore, ∠ B = 5x - 3 = 50 - 3 = 47°  

Now, we know that in a parallelogram the adjacent angles are supplementary i.e. ∠ A + ∠ B = 180°

⇒ ∠ A = 180 - ∠ B = 180° - 47° = 133°

Therefore, ∠ DAB = 133° (Answer)