Question

1. the angle measures of a triangle are 4x + 16 degrees, 5x - 1 degress, and x + 15 degrees. which of the following is not one of the angles meausres of the triangle? a) 30 b) 75 c) 74 d) 76 alternate exterior angles theorem

Explanation:

Step1: Use the triangle angle - sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \((4x + 16)+(5x-1)+(x + 15)=180\).
Combine like terms: \(4x+5x+x+16 - 1+15=180\), which simplifies to \(10x+30 = 180\).

Step2: Solve for \(x\)

Subtract \(30\) from both sides: \(10x=180 - 30=150\).
Divide both sides by \(10\): \(x=\frac{150}{10}=15\).

Step3: Find the measures of the angles

For the first angle: \(4x + 16\), substitute \(x = 15\), we get \(4\times15+16=60 + 16=76^{\circ}\).
For the second angle: \(5x-1\), substitute \(x = 15\), we get \(5\times15-1=75 - 1=74^{\circ}\).
For the third angle: \(x + 15\), substitute \(x = 15\), we get \(15+15=30^{\circ}\).

Answer:

A. \(30\), C. \(74\), D. \(76\) are the angle measures of the triangle. So the answer is B.