Question

Question 16
If two adjacent angles of a parallelogram are $(5x-5{)}^{\circ }$ and $(10x+35{)}^{\circ }$, then the ratio of these angles is ___________.
a) 1 : 3
b) 2 : 3
c) 1 : 4
d) 1 : 2

Answer 1

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.