Question

A triangle has two angles that measure 85 and 23. Which has to be the measure of the third angle?

Answer 1

Step-by-step explanation:

Given :-

• A triangle have two angles that measures 85° and 23°.

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,

$\sf \longrightarrow {\angle{A}\ +\ \angle{B}\ +\ \angle{C}\ =\ 180^{\circ}}$

$\sf \longrightarrow {85^{\circ}\ +\ 23^{\circ}\ +\ x\ =\ 180^{\circ}}$

$\sf \longrightarrow {108^{\circ}\ +\ x\ =\ 180^{\circ}}$

$\sf \longrightarrow {x\ =\ 180^{\circ}\ -\ 108^{\circ}}$

$\bf \longrightarrow {\underline{x\ =\ 72^{\circ}}}\ \bigstar$

∴ Hence, the measure of the third angle of the triangle is 72°.