Two adjacent angles of a parallelogram are 5x - 5 and (10x + 35 then the value of x is)

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Question 16 If two adjacent angles of a parallelogram are 5 x 5∘ and 10 x +35∘, then the ratio of these angles isa 1: 3b 2: 3c 1: 4d 1: 2

Solution

We know that the adjacent angles of a parallelogram are supplementary, i.e. their sum is equal to ${180}^{\circ }$,
$\therefore (5x-5)+(10x+35)={180}^{\circ }\Rightarrow 15x+{30}^{\circ }={180}^{\circ }\Rightarrow 15x={150}^{\circ }\Rightarrow x={10}^{\circ }$
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.