Question

Find the the measure of all the of a parallelogram ,if one angle is 15° less than twice the smallest angle.

Answer 1

Step-by-step explanation:

Let one angle be x

Therefore other angle will be 2x-15

Now,

x+x+2x-15+2x-15=360 [Angle sum property}

6x-30=360

6x=360+60

x=390/6

x=65°

2x-15 =2*65-15

130-15=115°

Therefore all angles are 65°,65°,115,°115°

Answer 2

Let ABCD be a parallelogram.

Let angle one be x° 【 Let angle A be x°】

Therefore other angle be 2x -15° 【 Let angle B be 2x-15°】

Now ,

x + 2x-15 + x + 2x-15 = 360° (angle sum property)

$= 6x - 30 = 360° \\ </p><p>= 6x = 360 + 30 \\ </p><p>=6x = 390 \\ </p><p>= x = \frac{390}{6} \\ </p><p> = x = 65$

x = 65°

i .e . angle A = 65°

Now,

$2x \: - 15 = 2 \times 65 - 15 \\ = 130 - 15 \\ = 115$

i .e . angle B = 115°

Now ,

angle C = 65° ( opposite angle)

And angle D = 115° ( opposite angle)