Question

Find angle x and angle y:

If $\angle$A = ${40}^{\circ }$​, $\angle$B = ${80}^{\circ }$​, and x = $\angle$C+y. Then the value of angle x & y in degrees is:

• A. True
• B. False
• C. $y={80}^{\circ }$
• D. $y={30}^{\circ }$

Answer 1

Answer: (A), (D)

The correct options are
A

True

D $y={30}^{\circ }$

$\angle$C = ${180}^{\circ }-({40}^{\circ }+{80}^{\circ }$)​
$\therefore$$\angle$C=${60}^{\circ }$
and $x=\angle$C+y......................(1)
$\because$
$\angle$C + $\angle$C+$\angle$y+ $\angle$y = ${180}^{\circ }$​
$\therefore$ ​
=> $2\angle$C + $2\angle$y = $2\times ({60}^{\circ }+y^{\circ })$
=> ${120}^{\circ }+2y^{\circ }={180}^{\circ }$
$\therefore$$y={30}^{\circ }$
$\therefore x={60}^{\circ }+{30}^{\circ }$
$x={90}^{\circ }$