Question

Find the sizes of the angles of the parallelogram if one of the angle is 20 degree less than twice the smallest angle

Answer 1

Answer:

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Answer 2

Step-by-step explanation:

Given:

• One angle of parallogram is 20° less than twice the smallest angle.

To Find:

• Measure of angles of parallelogram

Solution: Let the smallest angle be x°

∴ Another angle will be = (2x – 20)°

• These two angles are Adjacent to each other.

• We know that Adjacent angles of parallelogram measures 180°.

Therefore,

$\small\implies{\sf }$ (2x – 20)° + x° = 180°

$\small\implies{\sf }$ 2x + x – 20° = 180°

$\small\implies{\sf }$ 3x – 20° = 180°

$\small\implies{\sf }$ 3x = 180° + 20°

$\small\implies{\sf }$ 3x = 200°

$\small\implies{\sf }$ x = 200/3

$\small\implies{\sf }$ x = 66.67°

Hence, measure of smallest angle is x° = 66.67°

∴ Another angle will be (2x – 20)° = 2 x 66.67 –20

$\small\implies{\sf }$ 133.34 – 20

$\small\implies{\sf }$ 113.34 cm

Hence measure of another angle will be 113.34 cm

_______________________

★ We know that the opposite angles of parallogram are equal and sum of all angles is 180° ★

→ 113.34 + 113.34 + 66.67 + 66.67 = 360

→ 360.02 = 360°

→ 360° = 360°