Question

19. Quadrilateral ABCD is a parallelogram. What is the measure of ZDAB? Show your work.

A

B.

5x-3

3x+17

D

С

Answer 1

∠DAB = 133°

Explanation:

Given - Quadrilateral ABCD is a parallelogram. ∠D = 3x + 17, ∠B = 5x - 3

To find - What is the measure of ∠DAB?

Proof -

We know that In a parallelogram, opposite angles are equal.

So, ∠A = ∠C and ∠B = ∠D

Now,

As ∠B = ∠D

⇒3x + 17 = 5x - 3

⇒17 + 3 = 5x - 3x

⇒20 = 2x

⇒x = 10

So,

∠B = 5(10) - 3 = 50 - 3 = 47

⇒∠B = 47°

Also, we know that

∠A + ∠B = 180°

⇒∠A = 180° - ∠B

⇒∠A = 180° - 47° = 133°

⇒∠A = 133°

⇒∠DAB = 133°