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Q.

If two adjacent angles of a parallelogram are in the ratio 1:5, then determine the measures of all the angles of the parallelogram.

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a

30°, 150°, 30°, 150°

b

85°, 95°, 85°, 95°

c

45°, 135°, 45°, 135°

d

30°, 180°, 30°, 180°

answer is A.

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Detailed Solution

Given, two adjacent angles of a parallelogram are in the ratio 1:5.
The parallelogram holds the property of adjacent angles being supplementary.
Using this property, we will determine the angle measures of the parallelogram whose two adjacent angles are in the ratio of 1:5.
So, as the adjacent angles are supplementary, then their sum must be

180 ∘

.
Thus, we have,

x + 5 x = 180 ° 6 x = 180 ° x = 30 °

So, we have, the value of the other adjacent angle as

5 × 30 ∘ = 150 ∘

.
Next, we know that opposite angles in a parallelogram are equal.
So, the two remaining angles for the given parallelogram will also be

30 °

and

150 °

respectively.
So, the correct option is (1).

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