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 $=50^{\circ}$
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 $=115^{\circ}$
Sum of interior angles $=x+50^{\circ}$
Using exterior angle theorem, we have,
$115^{\circ}=x+50^{\circ}$
$x=115^{\circ}-50^{\circ}$
$x=65^{\circ}$
Hence, the value of $x$ is $65^{\circ}$
$1^{\text {st }}$ interior angle $=x$ and $2^{\text {nd }}$ interior angle $=50^{\circ}$
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 $=115^{\circ}$
Sum of interior angles $=x+50^{\circ}$
Using exterior angle theorem, we have,
$115^{\circ}=x+50^{\circ}$
$x=115^{\circ}-50^{\circ}$
$x=65^{\circ}$
Hence, the value of $x$ is $65^{\circ}$
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