Question

Consider the figure:

If $\angle A$= ${50}^{\circ }$​, $\angle B$ = ${70}^{\circ }$​, and x = 2y. Then the value of angle x & y in degrees is:

• A. 120
• B. $x={40}^{\circ }$
• C. $y={80}^{\circ }$
• D. $y={40}^{\circ }$

Answer 1

Answer: (A), (D)

The correct options are
A 120
D $y={40}^{\circ }$

$\angle C$ = ${180}^{\circ }-({50}^{\circ }+{70}^{\circ }$)​
$\therefore$$\angle C$=${60}^{\circ }$
and $x=2y$
$\because$
$\angle C$ + $\angle x$ + $\angle y$ = ${180}^{\circ }$​
$\therefore$ ​
=> $\angle C$ + $\angle x$ + $\angle y$ = ${60}^{\circ }+2y^{\circ }+y^{\circ }$
=> ${60}^{\circ }+3y^{\circ }={180}^{\circ }$
$\therefore$$y={40}^{\circ }$


Hence, $x=2y=2\times 40$
$\therefore x=80$