Question

In the parallelogram ABCD, m∠A = (8x + 8)°and m∠C = (9x − 7)°. Find the measure of each angle of this quadrilateral.

Answer 1

In the parallelogram ABCD,
m$\angle$A= (8x + 8)° and m$\angle$C = (9x − 7)°

$\Rightarrow$(8x + 8)°= ( 9x − 7)° (Opposite angles of a parallelogram are congruent)
$\Rightarrow$x = 15

So, the measures of different angles are:
m$\angle$A = 8 × 15 + 8 = 128°
m$\angle$C = 9 × 15 − 7 = 128°
m$\angle$A + m$\angle$D = 180° (Sum of adjacent angles of a parallelogram is 180°)
Thus, m$\angle$D = 52°
and
m$\angle$D = m$\angle$B (Opposite angles of a parallelogram are congruent)
So,
m$\angle$D = m$\angle$B = 52°
and m$\angle$A = m$\angle$C = 128°