Question

The measure of all the angles of a parallelogram, if one angle is $20°$ less than thrice the smallest angle is.

• A. $50°,130°,50°,130°$
• B. $60°,120°,60°,120°$
• C. $40°,60°,40°,60°$
• D. $80°,100°,80°,100°$

Answer 1

The correct option is A

$50°,130°,50°,130°$

Explanation for the correct option:

Properties of parallelogram

let smallest angle be $x°$
Then the other will be $(3x-20)°$
We know that adjacent angles of$\left|\right|gm$ are supplementary
therefore,
$$\begin{gathered} x+3x-20°={180}^{°} \\ \Rightarrow 4x=180°+20° \\ \Rightarrow 4x=200° \\ \Rightarrow x=200°/4 \\ \Rightarrow x=50° \end{gathered}$$
Other angle =$=3\times 50°-20°=130°$

So, the angles are $50°,130°,50°,130°$

Hence, the correct option is (A)