Question

find the measure of the third angle in the triangle. (assume ( a = 40^{circ} ) and ( b = 25^{circ} ).)

Explanation:

Step1: Recall the sum of angles in a triangle

The sum of the interior angles of a triangle is \(180^{\circ}\). Let the third - angle be \(x\). Then \(a + b+x=180^{\circ}\).

Step2: Substitute the given values of \(a\) and \(b\)

Given \(a = 40^{\circ}\) and \(b = 25^{\circ}\), we substitute into the formula: \(x=180-(a + b)\).

$$x=180-(40 + 25)$$

Step3: Calculate the value of \(x\)

First, calculate \(40+25 = 65\). Then \(x=180 - 65\).

$$x = 115^{\circ}$$

Answer:

\(115\)