Question

One angle of a parallelogram is twice the adjacent angle. Form the linear equations in two variables and find the measures of angles of the parallelogram.

• A. ${60}^{\circ }$, ${100}^{\circ }$, ${180}^{\circ }$, ${20}^{\circ }$
• B. ${140}^{\circ }$, ${20}^{\circ }$, ${120}^{\circ }$, ${80}^{\circ }$
• C. ${60}^{\circ }$, ${120}^{\circ }$, ${60}^{\circ }$, ${120}^{\circ }$
• D. ${100}^{\circ }$, ${80}^{\circ }$, ${100}^{\circ }$, ${80}^{\circ }$

Answer 1

The correct option is C

${60}^{\circ }$, ${120}^{\circ }$, ${60}^{\circ }$, ${120}^{\circ }$

Let one angle be x and adjacent angle be y.
Given, x = 2y--- (i)

Sum of adjacent angles of a parallelogram is ${180}^{\circ }$
$\Rightarrow$ x + y = ${180}^{\circ }$---- (ii)

Substitute the value of x from (i) in (ii), we get
$\Rightarrow$ 2y + y = 180°
$\Rightarrow$ 3y = 180°
$\therefore$ y = $\frac{180°}{3}=60°$
y = ${60}^{\circ }$

$\Rightarrow$ x = 2y
$\Rightarrow$ x = 2(60)
$\Rightarrow$​ x = ${120}^{\circ }$