find the measure of each angle of a parallelogram, if one of its angle is 30 degree less than twice - Maths - Quadrilaterals

Question

find the measure of each angle of a parallelogram, if one of its
angle is 30 degree less than twice of the smallest angle

Lalit Mehra · Accepted Answer

Hi!
Here is the answer to your question
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"https://s3mn%20mnimgs%20com/img/shared/userimages/mn_images/image/a4(13)%20png"
alt="">
Let ∠A be the smallest angle of the parallelogram
ABCD
∠A = ∠C (opposite angles of parallelogram are
equal)
∠B = ∠D (opposite angles of parallelogram are
equal)
Given, ∠B = 2∠A – 30°
∠A + ∠B = 180° (sum of consecutive interior angles
is supplementary)
⇒ ∠A + (2∠A – 30°) = 180°
⇒ 3∠A = 210°
⇒∠A = 70
∴∠B = 2 × 70° –
30° = 140° – 30° = 110°
Thus, ∠A = ∠C = 70° and ∠B = ∠D =
110°
Cheers!

find the measure of each angle of a parallelogram, if one of its angle is 30 degree less than twice of the smallest angle.