Step-by-step explanation:
Given :-
- In a triangle, two of the angles measure 63° and 71°.
To Find :-
- Measure of the third angle.
Solution :-
Let the measure of the third angle of the triangle be x.
As we know that,
- The sum of all three sides of a triangle is 180° which is the angle sum property of triangle.
Therefore,
\(\sf \longrightarrow {\angle{A}\ +\ \angle{B}\ +\ \angle{C}\ =\ 180^{\circ}}\)
\(\sf \longrightarrow {63^{\circ}\ +\ 71^{\circ}\ +\ x\ =\ 180^{\circ}}\)
\(\sf \longrightarrow {134^{\circ}\ +\ x\ =\ 180^{\circ}}\)
\(\sf \longrightarrow {x\ =\ 180^{\circ}\ -\ 134^{\circ}}\)
\(\bf \longrightarrow {\underline{x\ =\ 46^{\circ}}}\ \bigstar\)
∴ Hence, the measure of the third angle of triangle is 46°.
