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
[tex] (8x-8)+(17x+13)= 180 [/tex]
[tex] 8x-8+17x+13= 180 [/tex]
Combine the like terms,
[tex] 25x +5 = 180 [/tex]
Subtract 5 from both sides
[tex] 25x= 175 [/tex]
Divide both sides by 25
[tex] x= 7 [/tex]
Now using the value of x , we can first find the measure of angle D
∠D= [tex] 17x+13= 17(7)+13 = 119+13 = 132 [/tex]
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°
