Question

geometry
name
ws \triangle angle sum theorem\
date
find the measure of each angle indicated.
1)
2)
3)
4)
5)
6)
7)
8)
9)
10)

Explanation:

Step1: Recall the triangle angle sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). Let the unknown angle be \(x\). Then \(x + \text{known angle}_1+\text{known angle}_2 = 180^{\circ}\), so \(x=180^{\circ}-\text{known angle}_1 - \text{known angle}_2\)

Step2: Calculate each unknown angle

1. \(x = 180^{\circ}-50^{\circ}-81^{\circ}=49^{\circ}\)
2. \(x = 180^{\circ}-64^{\circ}-54^{\circ}=62^{\circ}\)
3. \(x = 180^{\circ}-40^{\circ}-95^{\circ}=45^{\circ}\)
4. \(x = 180^{\circ}-65^{\circ}-60^{\circ}=55^{\circ}\)
5. \(x = 180^{\circ}-35^{\circ}-85^{\circ}=60^{\circ}\)
6. \(x = 180^{\circ}-33^{\circ}-97^{\circ}=50^{\circ}\)
7. \(x = 180^{\circ}-70^{\circ}-30^{\circ}=80^{\circ}\)
8. \(x = 180^{\circ}-100^{\circ}-30^{\circ}=50^{\circ}\)
9. \(x = 180^{\circ}-90^{\circ}-35^{\circ}=55^{\circ}\)
10. \(x = 180^{\circ}-35^{\circ}-80^{\circ}=65^{\circ}\)

Answer:

1. \(49^{\circ}\)
2. \(62^{\circ}\)
3. \(45^{\circ}\)
4. \(55^{\circ}\)
5. \(60^{\circ}\)
6. \(50^{\circ}\)
7. \(80^{\circ}\)
8. \(50^{\circ}\)
9. \(55^{\circ}\)
10. \(65^{\circ}\)