Question

1. ABCD is a parallelogram. Find the value of x.

Answer 1

In a parallelogram, opposite angles are congruent.
B = D

B = 7x - 31
D = 5x + 13

7x - 31 = 5x + 13
7x - 5x = 13 + 31
2x = 44
x = 44/2
x = 22  Choice B.

B = 7x - 31 = 7(22) - 31 = 154 - 31 = 123
B = D ; D = 123°

Consecutive angles are complementary. A + D = 180°

A = 180 - 123
A = 57°

Answer on question 2. A. Two of the angles measure 57°, and the other two measure 123°.

Answer 2

Answer:

Step-by-step explanation:

1. Since, it is given that ABCD is a parallelogram, therefore opposite angles of parallelogram are equal, hence

∠B=∠D

⇒7x-31=5x+13

⇒2x=44

⇒x=22

Hence, option B is correct.

2. Since, we get x=22, therefore

∠B=7x-31=7(22)-31=154-31=123°

∠B=123°

and ∠D=5x+13=5(22)+13=123°

∠D=123°

Also, ∠A+∠D=180°(corresponding angles)

⇒∠A=180-123

⇒∠A=57°

Now, ∠A=∠C=57°(opposite angles of parallelogram)

thus, Two of the angles measure 57°, and the other two measure 123°.

Therefore, option A is correct.