Question

Consider the figure:

If $\angle$1 = ${80}^{\circ }$, $\angle$2 = ${70}^{\circ }$, and x = ${10}^{\circ }$+y, then find the value of $\angle$x (in degrees).

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• A. 70
• B. $\angle$x=${70}^{\circ }$
• C. $\angle$x=${80}^{\circ }$
• D. $\angle$x=${60}^{\circ }$

Answer 1

The correct option is C $\angle$x=${80}^{\circ }$

Given, $\angle$1 = ${80}^{\circ }$​
Hence, $\angle$2 = ${70}^{\circ }$​
We know that $\angle$C+$\angle$1+$\angle$2=${180}^{\circ }$​
$\angle x+\angle y+\angle C={180}^{\circ }$ [Angle sum property of the triangle]
Substiuting the given values, we have,
$\angle$1 = ${80}^{\circ }$​
$\angle$2 = ${70}^{\circ }$​
$\therefore$$\angle$C=${180}^{\circ }$ - [$\angle$1+$\angle$2]
​$\angle$C=${180}^{\circ }$ - [${80}^{\circ }$+${70}^{\circ }$]

​​$\angle$C=${30}^{\circ }$

According to the question:-
x = ${10}^{\circ }$+y
also,$\angle$C+$\angle$x+$\angle$y=${180}^{\circ }$...........................................[angle sum property of the triangle]
​$\therefore$${30}^{\circ }+{10}^{\circ }$+$\angle$y+$\angle$y=${180}^{\circ }$

${30}^{\circ }+{10}^{\circ }$+$2\angle$y=${180}^{\circ }$
​$\therefore$$\angle$y=${70}^{\circ }$

and $\angle$x=${10}^{\circ }$+${70}^{\circ }$
​$\therefore$$\angle$x=${80}^{\circ }$