Two adjacent angles of a parallelogram are as 1: 2. Find the measures of all the angles of the parallelogram.

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°, 130 °, 50 °, 130 °

°, 120 °, 60 °, 120 °

°, 140 °, 40 °, 140 °

°, 150 °, 30 °, 150 °

answer is A.

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Detailed Solution

Let us consider one adjacent angle is

x o

.
And, the other adjacent angle is

2 x o

.
As we know that the sum of adjacent angles in a parallelogram is

180 °

∴ x ° + 2 x ° = 180 ° ⇒ 3 x ° = 180 ° ⇒ x = 1803 ⇒ x = 60 °

Then,

2 x = 2 × 60 ⇒ 2 x = 120 °

Also, the opposite angles are equal in a parallelogram.
So, the measures of each angle are

60 °, 60 °, 120 °, 120 °

Hence, the correct option is 1.

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