Question

The adjacent interior angles of a parallelogram are$(2x–15)°$ and $(7x–75)°$. Find all the angles of parallelogram.

• A. $45°,135°,45°,135°$
• B. $50°,130°,50°,130°$
• C. $40°,140°,40°,140°$
• D. None of these

Answer 1

The correct option is A

$45°,135°,45°,135°$

Explanation for the correct option:

Finding the value of $x$:

It is given that the adjacent interior angles of a parallelogram are$(2x–15)°$ and $(7x–75)°$.

Let the angles of the parallelogram be $\angle A,\angle B,\angle C$ and $\angle D$ where $\angle A=(2x-15)°$ and $\angle B=(7x-75)°$.

$\because$Sum of two adjacent interior angles of a parallelogram is $180°$

$$\begin{gathered} \Rightarrow \angle A+\angle B=180° \\ \Rightarrow (2x–15)°+(7x–75)°=180° \\ \Rightarrow 9x–90°=180° \\ \Rightarrow 9x=180°+90° \\ \Rightarrow 9x=270° \\ \Rightarrow x=\frac{270°}{9} \\ \therefore x=30° \end{gathered}$$

Finding the angles of the parallelogram:

$$\begin{gathered} \angle A=(2x–15)° \\ \angle A=2\times 30°–15° \\ \angle A=60°-15° \\ \angle A=45° \end{gathered}$$

$$\begin{gathered} \angle B=(7x–75)° \\ \angle B=7\times 30°–75° \\ \angle B=210°-75° \\ \angle B=135° \end{gathered}$$

$\because$Opposite angles of a parallelogram are equal

$\Rightarrow \angle A=\angle C=45°$

and $\angle B=\angle D=135°$

Therefore, the angles of the parallelogram are $45°,135°,45°,135°$.

Hence, option (A) is the correct answer.