Question

Two opposite angles of a parallelogram are $(4x-3{)}^{\circ }$and $(57-x{)}^{\circ }$. Find the measure of each angle of the parallelogram. [2 MARKS]

Answer 1

Concept : 1 Mark
Calculation : 1 Mark

Since opposite angles of a parallelogram are equal.

$\Rightarrow (4x–3{)}^{\circ }=(57–x{)}^{\circ }$

$5x=60$

$x=12$


$\therefore$ two angles are equal to $(4x-3{)}^{\circ }=(4\times 12-3{)}^{\circ }=(48-3{)}^{\circ }={45}^{\circ }$

The other pair will be equal to ${180}^{\circ }$ - ${45}^{\circ }$ = ${135}^{\circ }$
[Since adjacent angles are supplementary]

$\therefore$ angles are ${45}^{\circ }$, ${45}^{\circ }$, ${135}^{\circ }$ and ${135}^{\circ }$