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 \(180^{\circ}\).

Step2: Calculate each angle

1. Let the unknown angle be \(x\). Then \(x + 50^{\circ}+81^{\circ}=180^{\circ}\), so \(x=180^{\circ}-(50^{\circ}+81^{\circ}) = 49^{\circ}\).
2. Let the unknown angle be \(y\). Then \(y+64^{\circ}+54^{\circ}=180^{\circ}\), so \(y = 180^{\circ}-(64^{\circ}+54^{\circ})=62^{\circ}\).
3. Let the unknown angle be \(z\). Then \(z + 40^{\circ}+95^{\circ}=180^{\circ}\), so \(z=180^{\circ}-(40^{\circ}+95^{\circ}) = 45^{\circ}\).
4. Let the unknown angle be \(a\). Then \(a+65^{\circ}+60^{\circ}=180^{\circ}\), so \(a=180^{\circ}-(65^{\circ}+60^{\circ}) = 55^{\circ}\).
5. Let the unknown angle be \(b\). Then \(b+35^{\circ}+85^{\circ}=180^{\circ}\), so \(b=180^{\circ}-(35^{\circ}+85^{\circ}) = 60^{\circ}\).
6. Let the unknown angle be \(c\). Then \(c+33^{\circ}+97^{\circ}=180^{\circ}\), so \(c=180^{\circ}-(33^{\circ}+97^{\circ}) = 50^{\circ}\).
7. Let the unknown angle be \(d\). Then \(d+70^{\circ}+30^{\circ}=180^{\circ}\), so \(d=180^{\circ}-(70^{\circ}+30^{\circ}) = 80^{\circ}\).
8. Let the unknown angle be \(e\). Then \(e+100^{\circ}+30^{\circ}=180^{\circ}\), so \(e=180^{\circ}-(100^{\circ}+30^{\circ}) = 50^{\circ}\).
9. Let the unknown angle be \(f\). Since it's a right - triangle (\(90^{\circ}\)), then \(f+25^{\circ}+90^{\circ}=180^{\circ}\), so \(f=180^{\circ}-(25^{\circ}+90^{\circ}) = 65^{\circ}\).
10. Let the unknown angle be \(g\). Then \(g+35^{\circ}+80^{\circ}=180^{\circ}\), so \(g=180^{\circ}-(35^{\circ}+80^{\circ}) = 65^{\circ}\).

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. \(65^{\circ}\)
10. \(65^{\circ}\)