Question

Find the measure of all four angles of a parallelogram whose consecutive angles are in the ratio 1 :3​

Answer 1

Answer:

Solution: Given consecutive angles of a parallelogram are in the ratio 1:3Therefore, the two consecutive anglesbe x and 3x. X + 3x = 180° (sum of the interior angles on the same side of the transversal is 1809 4x = 180° x = 45° Therefore the two consecutive anglesare 45° and 3(459) = 135º.

Answer 2

Answer:

135°

Step-by-step explanation:

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°.