Question

The value of $\angle x$ is

• A. ${100}^{\circ }$
• B. ${110}^{\circ }$
• C. ${120}^{\circ }$
• D. ${130}^{\circ }$

Answer 1

The correct option is C ${120}^{\circ }$

Using the angle sum property of a triangle, we know that the sum of all the interior angles of a triangle must be ${180}^{\circ }$.

Hence, the $3^{rd}$ angle of the triangle measures ${180}^{\circ }-({50}^{\circ }+{70}^{\circ })$
$={180}^{\circ }-\left({120}^{\circ }\right)={60}^{\circ }$

Now, we know that the sum of the angles that lie on a straight line sum upto ${180}^{\circ }$

$\therefore x+{60}^{\circ }={180}^{\circ }$
$x={120}^{\circ }$

Alternatively, we can directly apply the "Exterior angle property" of a triangle which states that: "An exterior angle of a triangle is equal to the sum of the two opposite interior angles"

Using this property, we get,
$x={50}^{\circ }+{70}^{\circ }$
$x={120}^{\circ }$