Question

triangle sum theorem - in a triangle, the 3 ____ angles sum to ____

examples: solve for x. then find all missing angles. triangles may not be drawn to scale.

1.

2.

4.

Explanation:

Step1: Apply Triangle Sum Theorem

For the first triangle, using \(m\angle A + m\angle B + m\angle C=180^{\circ}\), we have \(75^{\circ}+59^{\circ}+x^{\circ}=180^{\circ}\).

Step2: Solve for \(x\)

\(x = 180-(75 + 59)=180 - 134=46\).

Step3: Apply Triangle Sum Theorem for the second triangle

For the second triangle, \(74^{\circ}+39^{\circ}+x^{\circ}=180^{\circ}\).

Step4: Solve for \(x\)

\(x=180-(74 + 39)=180 - 113 = 67\).

Answer:

1. \(x = 46\)
2. \(x = 67\)