Question

If two adjacent angles of a parallelogram are $(5x-5)°$and $(10x+35)°,$then the ratio of these angles is

• A. $1:3$
• B. $2:3$
• C. $1:4$
• D. $1:2$

Answer 1

The correct option is A

$1:3$

Explanation for the correct options:

Step $1:$ Solve for the value of $x.$

Given: Two adjacent angles are $\angle A$ be $(5x-5)°$and $(10x+35)°,$

The sum of any two adjacent angles of a parallelogram is equal to $180°.$

$\Rightarrow (5x-5)°+(10x+35)°=180°$

$\Rightarrow$ $15x+30=180$

$\Rightarrow$ $15x=150$

$\Rightarrow$ $x=10°$

Step $2:$ Solve for the ratio of the angles of a parallelogram.

Put the value of $x$ in $(5x-5)°$ and $(10x+35)°$

$$\begin{gathered} (5x-5)°=(5\times 10-5)° \\ =45° \\ (10x+35)°=(10\times 10+35)° \\ =135° \end{gathered}$$

$\therefore$The ratio of the angles of parallelogram $=\frac{\left(5x-5\right)°}{\left(10x+35\right)°}$

$$\begin{gathered} =\frac{45°}{135°} \\ =\frac{1}{3} \end{gathered}$$

The angles $45°$ and $135°$ are in the ratio of $1:3.$

Hence two adjacent angles of a parallelogram are $(5x-5)°$and $(10x+35)°,$then the ratio of these angles is $1:3.$