Question

name:
date:
quiz: interior angles of a triangle
directions: solve for the given variable, label all angles and identify what type of triangle it
is. ( not drawn to scale )
1)
2)

Explanation:

Step1: Use the triangle angle - sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). For the first triangle: \((x + 5)+(6x-15)+(4x + 25)=180\).
Combine like terms: \(x+5+6x - 15+4x+25=180\), \((x+6x + 4x)+(5-15 + 25)=180\), \(11x+15 = 180\).
Subtract 15 from both sides: \(11x=180 - 15\), \(11x=165\).
Divide both sides by 11: \(x=\frac{165}{11}=15\).
Then find the angles:

• \(x + 5=15+5 = 20^{\circ}\)
• \(6x-15=6\times15-15=90 - 15=75^{\circ}\)
• \(4x + 25=4\times15+25=60+25 = 85^{\circ}\)

For the second triangle: \(6x+(3x + 20)+x=180\).
Combine like terms: \((6x+3x+x)+20=180\), \(10x+20 = 180\).
Subtract 20 from both sides: \(10x=180 - 20\), \(10x=160\).
Divide both sides by 10: \(x = 16\).
Then find the angles:

• \(6x=6\times16=96^{\circ}\)
• \(3x + 20=3\times16+20=48+20=68^{\circ}\)
• \(x=16^{\circ}\)

Answer:

1. \(x = 15\), angles are \(20^{\circ}\), \(75^{\circ}\), \(85^{\circ}\), and it is an acute triangle.
2. \(x = 16\), angles are \(96^{\circ}\), \(68^{\circ}\), \(16^{\circ}\), and it is an obtuse triangle.