Question

1. solve for x. 14) 15)

Explanation:

Step1: Use the triangle angle - sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\).
For the first triangle (14):
\((8x + 3)+70 + 75=180\)
Combine like terms: \(8x+3 + 145=180\), so \(8x+148 = 180\)
Subtract 148 from both sides: \(8x=180 - 148\), \(8x = 32\)
Divide both sides by 8: \(x=\frac{32}{8}=4\)

For the second triangle (15):
\((x + 71)+50+70 = 180\)
Combine like terms: \(x+71+120=180\), so \(x + 191=180\)
Subtract 191 from both sides: \(x=180 - 191=- 11\)

For the third triangle (16):
\((x + 71)+40 + 80=180\)
Combine like terms: \(x+71+120=180\), so \(x+191 = 180\)
Subtract 191 from both sides: \(x=180 - 191=-11\)

Answer:

For problem 14: \(x = 4\)
For problem 15: \(x=-11\)
For problem 16: \(x=-11\)