Question

finding angles ∠a and ∠b are supplementary. find ( mangle a ) and ( mangle b ). 11) ( mangle a = 3x ), ( mangle b = x + 8 ). 12) ( mangle a = 6x - 1 ), ( mangle b = 5x - 17 ).

Explanation:

Problem 11:

Step1: Recall supplementary angles sum to \(180^\circ\)

Since \(\angle A\) and \(\angle B\) are supplementary, \(m\angle A + m\angle B = 180^\circ\). Substitute \(m\angle A = 3x\) and \(m\angle B = x + 8\):
\(3x + (x + 8) = 180\)

Step2: Solve for \(x\)

Simplify the equation:
\(4x + 8 = 180\)
Subtract 8 from both sides:
\(4x = 172\)
Divide by 4:
\(x = 43\)

Step3: Find \(m\angle A\) and \(m\angle B\)

\(m\angle A = 3x = 3(43) = 129^\circ\)
\(m\angle B = x + 8 = 43 + 8 = 51^\circ\)

Problem 12:

Step1: Use supplementary angles property

\(m\angle A + m\angle B = 180^\circ\). Substitute \(m\angle A = 6x - 1\) and \(m\angle B = 5x - 17\):
\((6x - 1) + (5x - 17) = 180\)

Step2: Solve for \(x\)

Simplify:
\(11x - 18 = 180\)
Add 18 to both sides:
\(11x = 198\)
Divide by 11:
\(x = 18\)

Step3: Calculate angle measures

\(m\angle A = 6x - 1 = 6(18) - 1 = 107^\circ\)
\(m\angle B = 5x - 17 = 5(18) - 17 = 73^\circ\)

Answer:

s:

1. \(m\angle A = 129^\circ\), \(m\angle B = 51^\circ\)
2. \(m\angle A = 107^\circ\), \(m\angle B = 73^\circ\)