Question

Find the measure of all four angle of
a parallelogram whose consecutive angle
a are in the ratio:1:3
90°
45°
180°​

Answer 1

The ratio of two consecutive angles of a parallelogram = 1 : 3

Let x and 3x be the two consecutive angles.

We know that the sum of interior angles on the same side of the transversal is 180°.

Therefore, x + 3x = 180°

4x = 180°

x = 180°/4

x = 45°

⇒ 3x = 3(45°) = 135°

Thus, the measure of two consecutive angles is 45° and 135°.

As we know, the opposite angles of a parallelogram are equal.

Hence, the measure of all the four angles is 45°, 135°, 45°, and 135°.

Step-by-step explanation:

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Answer 2

The ratio of two consecutive angles of a parallelogram = 1 : 3

Let x and 3x be the two consecutive angles.

Let x and 3x be the two consecutive angles.We know that the sum of interior angles on the

same side of the transversal is 180°.

Therefore,

$\longmapsto\tt{ x + 3x = 180°}$

$\longmapsto\tt{4x = 180°}$

$\longmapsto\tt{x = 180°/4}$

$\longmapsto\tt{x = 45°}$

$\longmapsto\tt{⇒ 3x = 3(45°) = 135°}$

Thus, the measure of two consecutive angles is 45° and 135°.

As we know,

the opposite angles of a parallelogram are equal.

Hence, the measure of all the four angles is 45°, 135°, 45°, and 135°.