If two adjacent angles of a parallelogram are (5x−5)∘ and (10x+35

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Question

If two adjacent angles of a parallelogram are

(5 x - 5)^{\circ}

and

(10 x + 35)^{\circ}

, then the ratio of these angles is ___________.
a) 1 : 3
b) 2 : 3
c) 1 : 4
d) 1 : 2

Answer:
:
We know that the adjacent angles of a parallelogram are supplementary, i.e. their sum is equal to

180^{\circ}

,

∴ (5 x - 5) + (10 x + 35) = 180^{\circ} \Rightarrow 15 x + 30^{\circ} = 180^{\circ} \Rightarrow 15 x = 150^{\circ} \Rightarrow x = 10^{\circ}

Thus, the angles are

(5 \times 10 - 5) = 45^{\circ}

and

(10 \times 10 + 35) = 135^{\circ}

.
Hence, the required ratio is

45^{\circ} : 135^{\circ}

, that is, 1 : 3.

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