Question
Find the value of the unknown interior angle $x$ in the figure:
✓
Answer
Given that,
$1^{\text {st }}$ interior angle $=x$ and, $2^{\text {nd }}$ interior angle $=60^{\circ}$
Now, According to exterior angle theorem:
The measure of an exterior angle of a triangle is equal to the sum of the measure of the two non-adjacent interior angles of the triangle.
Here, Exterior angle $=120^{\circ}$
Sum of interior angles $=x+60^{\circ}$
Using exterior angle theorem, we have
$120^{\circ}=x+60^{\circ}$
$x=120^{\circ}-60^{\circ}$
$x=60^{\circ}$
Hence, the value of $x$ is $60^{\circ}$
$1^{\text {st }}$ interior angle $=x$ and, $2^{\text {nd }}$ interior angle $=60^{\circ}$
Now, According to exterior angle theorem:
The measure of an exterior angle of a triangle is equal to the sum of the measure of the two non-adjacent interior angles of the triangle.
Here, Exterior angle $=120^{\circ}$
Sum of interior angles $=x+60^{\circ}$
Using exterior angle theorem, we have
$120^{\circ}=x+60^{\circ}$
$x=120^{\circ}-60^{\circ}$
$x=60^{\circ}$
Hence, the value of $x$ is $60^{\circ}$
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