Question

In a parallelogram ABCD, angleD = 115°, determine the measure of angleA and angleB.​

Answer 1

Answer:

angle A = 65° and angle B = 115°

Step-by-step explanation:

sum of all angle of quadrilateral is 360°

angle A + angle B+ angle C +Angle D = 360°

(opposite angle in parallelogram are equal )

Angle A + 115°+ Angle A + 115°= 360°

2*Angle A = 360°-230

2*Angle A = 130°

Angle A = 65°

therefore , angle A =angle C = 65°

Angle B = angle D = 115°

Answer 2

Answer:

Angle A = 65 degree

Angle B = 115 degree

Step-by-step explanation:

In parallelogram ABCD,

Angle D = 115 degree

We know that,

"Opposite angles of Parallelogram are congruent"

Therefore,

Angle D = Angle C

i.e. Angle D = Angle C = 115 degree

Now,

Angle A = 180 - Angle B --------- (Angles in linear pair)

Angle A = 180 - 115

Angle A = 65  

Therefore, Angle A = 65 degree

To know whether our answer is correct,

We know that,

"Measures of all angles of Parallelogram is 360 degree".

Therefore,

Angle A + Angle B + Angle C + Angle D = 360

65 + 115 + 65 + 115 = 360

Therefore, Our answer is correct.