Question

an obtuse angle of an rhombus is twice the acute angle by 30' find the measure of each angle​

Answer 1

Answer:

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Answer 2

Answer:

Angle A = Angle C = 130° &

Angle B = Angle D = 50°

Step-by-step explanation:

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✔The opposite angles of a rhombus are congruent _______(1)

✔& Adjacent angles of of a rhombus are supplementary _________(2)

Let,□ABCD is a rhombus.

Angle A = Angle C

Angle B = Angle D

Now, Take angle A and angle B

Let, angle A is an obtuse angle and angle B is an acute angle.

Let, the common multiple be x..

Therefore,

Angle A is greater than Angle B by 30°

Angle B = x°

Angle A = (2x + 30)°

Angle A + Angle B = 180° ______(from 2)

2x + 30 + x = 180°

3x + 30 = 180°

3x = 180 – 30

3x = 150°

x = 150/3 = 50°

So, Angle B = 50°

Now,

Angle A = 2x + 30 = 2×50 + 30 = 130°

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Therefore,

Angle A = Angle C = 130° &

Angle B = Angle D = 50°

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