Question

1. two of the interior angles of a triangle are $50^{circ}$ and $75^{circ}$. which of the following is the measure of the third angle?

a. $50^{circ}$
b. $75^{circ}$
c. $125^{circ}$
d. $55^{circ}$

Explanation:

Step1: Recall triangle angle sum

The sum of interior angles of a triangle is \(180^\circ\).

Step2: Calculate the third angle

Let the third angle be \(x\). Then \(50^\circ + 75^\circ + x = 180^\circ\). First, add \(50^\circ\) and \(75^\circ\): \(50 + 75 = 125\). So, \(125^\circ + x = 180^\circ\). Subtract \(125^\circ\) from both sides: \(x = 180 - 125 = 55^\circ\).

Answer:

D. \(55^\circ\)