Question

In a parallelogram $\mathrm{ABCD}$ if $\angle \mathrm{D}=125°$ then find all other angles.

Answer 1

Using Properties of parallelogram

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

Given, $\angle \mathrm{D}=125°$

By property $1$,

$$\begin{gathered} \angle B=\angle D \\ \Rightarrow \angle B=125° \end{gathered}$$

By property $2$

$\begin{array}{cc}\Rightarrow & \angle A+\angle D=180°\\ \Rightarrow & \angle D=180°-125°\\ \Rightarrow & \angle A=55°\end{array}$

By property $1$

$$\begin{gathered} \angle C=\angle A \\ \Rightarrow \angle C=55° \end{gathered}$$

Hence, the value of the other angles are:

$\angle A=55°$

$\angle B=125°$

$\angle C=55°$