Question

In a parallelogram $\angle P=60°$ then other three angles are

• A. $45°,135°,120°$
• B. $60°,120°,120°$
• C. $60°,135°,135°$
• D. $45°,135°,135°$

Answer 1

The correct option is B

$60°,120°,120°$

1Explanation for the correct option:

1. Opposite angles of a parallelogram are equal.
2. Sum of adjacent angles of a parallelogram is $180°$.

Given, $\angle P=60°$.

By property 1,

$$\begin{gathered} \angle P=\angle R \\ \Rightarrow \angle R=60° \end{gathered}$$

By property 2,

$\begin{array}{cc}& \angle P+\angle Q=180°\\ \Rightarrow & \angle Q=120°\end{array}$

By property 1,

$$\begin{gathered} \angle Q=\angle S \\ \Rightarrow \angle S=120° \end{gathered}$$

So angles of parallelogram are $60°,120°,120°$.

Hence, option B is the correct option.