Question

The sum of two angles in a triangle total $62.5$ degrees. What is the other angle’s measure?

Answer 1

Hint: Here we are asked to find the measure of the third angle in a triangle when the sum of two other angles is given. The thing we need to know to solve this problem is, a triangle has three angles and the sum of its three angles will be equal to one hundred and eighty degrees. Since the sum of two angles is given, we will keep the third one as an unknown variable, and equating it to $180^\circ $ we will find the third angle.

Complete step by step answer:
It is given that the sum to two angles in a triangle total $62.5$ degrees we aim to find the third angle.
Before we solve this problem, we need to know some properties of a triangle. We know that the triangle has three sides and three angles. When we sum the measures of those three angles, we get the total as $180^\circ $ . That is if $\angle a,\angle b\& \angle c$ are the three angles of a triangle then $\angle a + \angle b + \angle c = 180^\circ $ .
Now let us take that $\angle p,\angle q\& \angle r$ as the angles of the given triangle. It is given that the sum of two angles equals $62.5$ degrees. Let $\angle p + \angle q = 62.5^\circ $ . We need to find the third angle that is $\angle r$ .
From the property of a triangle, we know that the sum of the angles will be equal one-eighty degrees.
So, we get $\angle p + \angle q + \angle r = 180^\circ $
We already know that $\angle p + \angle q = 62.5^\circ $ substituting it in the above we get
$62.5^\circ + \angle r = 180^\circ $
Now let us simplify the above to find the measure of the third angle.
$ \Rightarrow \angle r = 180^\circ - 62.5^\circ $
$ \Rightarrow \angle r = 117.5^\circ $
Thus, we got the third angle \[117.5^\circ \].

Note:
 In the above problem we have seen one of the properties of a triangle is that the sum of the measures of the angles of a triangle equals one hundred and eighty degrees. If the triangle is a right-angle triangle, then one of its angles will be equal to ninety degrees and if it is an isosceles triangle then two of its angles will be equal.