Question

ABCD is a parallelogram. Find the measure of

Answer 1

17x + 13 + 8x - 8 = 180

25x + 5 = 180

25x = 175

x = 7

/_A = /_C = 8(7)-8 = 56-7 = 49

Answer 2

In any parallelogram The sum of interior opposite angles on one side is 180°.

So it means the given two angles must add to 180°.

That is

$(8x-8)+(17x+13)= 180$

$8x-8+17x+13= 180$

Combine the like terms,

$25x +5 = 180$

Subtract 5 from both sides

$25x= 175$

Divide both sides by 25

$x= 7$

Now using the value of x , we can first find the measure of angle D

∠D= $17x+13= 17(7)+13 = 119+13 = 132$

So

∠D= 132°

Now we have to find the measure of angle A

Again using the same property we can say that

∠A+∠D= 180°

plug the value of angle D, so we get

∠A+132= 180

Subtract 132 from both sides

∠A= 180-132= 48°

So Measure of ∠A= 48°