Question

In the following triangle, find the value of $\angle y$ and $\angle z$, if $\angle x$ = ${50}^{\circ }$ and $\angle 2$ = ${60}^{\circ }$.

• A. $\angle y$ = ${70}^{\circ }$, $\angle z$ = ${60}^{\circ }$
• B. $\angle y$ = ${60}^{\circ }$, $\angle z$ = ${60}^{\circ }$
• C. $\angle y$ = ${60}^{\circ }$, $\angle z$ = ${70}^{\circ }$
• D. $\angle y$ = ${70}^{\circ }$, $\angle z$ = ${70}^{\circ }$

Answer 1

The correct option is A $\angle y$ = ${70}^{\circ }$, $\angle z$ = ${60}^{\circ }$

From the above figure, we see that,
$\angle x$ and $\angle 1$ are alternate interior angles.
In traingle ABC, $\overleftrightarrow{AB}$ $\parallel$ l.
Hence, $\angle x$ = $\angle 1$ = ${50}^{\circ }$ ,( as they are alternate interior angles)
$\angle 1$ + $\angle y$ + $\angle 2$ = $\angle 180$
(as they form a straight angle)
Given: $\angle 2$ = ${60}^{\circ }$
$\therefore$ $\angle 1$ + $\angle y$ + $\angle 2$ = ${50}^{\circ }$ + $\angle y$ + ${60}^{\circ }$ = ${180}^{\circ }$
$\Rightarrow$$\angle y$ = ${180}^{\circ }$ - ${110}^{\circ }$ =${70}^{\circ }$
The sum of the interior angles of a triangle = ${180}^{\circ }$
$\therefore$ $\angle x$ +$\angle y$ +$\angle z$ = ${180}^{\circ }$
${50}^{\circ }$ + ${70}^{\circ }$ + $\angle z$ = ${180}^{\circ }$
$\angle z$ = ${180}^{\circ }$ - ${120}^{\circ }$ = ${60}^{\circ }$