Question

In a parallelogram PQRD, ∠P=(2x+10) and ∠Q=(3x+29) Find all the angles of the parallelogram. ​

Answer 1

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In a parallelogram PQRD,

∠P=(2x+10) and ∠Q=(3x+30)

$\huge\underline\mathbb\purple{Answer:-}$

in this situation,

∠P & ∠Q are Adjacent angles.

Therefore,

Adjacent angles are supplementary.

∠P + ∠Q = 180

➡️ 2x+10 + 3x+30 = 180

➡️ 5x+ 40 = 180

➡️ 5x = 180 - 40

➡️ x = 140/5

➡️ x = 28

we know that,

1. ∠P=(2x+10) = 2×28+10

= 66

:- ∠P = 66°

2. ∠Q=(3x+30) = 3×28+30

= 114

:- ∠Q = 114°

Property of parallelogram is

1. opposite angle are congruet.

therefore:-

∠P = ∠R = 66°

∠Q = ∠D = 114°

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