Question

ABCD is a parallelogram is which $\angle ADC={70}^{\circ }$ and side AB is produced to point E as shown in the figure. Find $x+y.$

Answer 1

Here, $\angle C\text{and}\angle D$ are adjacent angles of the parallelogram

$\therefore \angle C+\angle D={180}^{\circ }$

$\Rightarrow x+{75}^{\circ }={180}^{\circ }$

$\Rightarrow x={105}^{\circ }$

$\text{Also,}y=x={105}^{\circ }\text{[alt. int. angles]}$

$\text{Thus,}x+y={105}^{\circ }+{105}^{\circ }={210}^{\circ }$