Question

∠a and ∠b are supplementary. find ( mangle a ) and ( mangle b ).

1. ( mangle a = x^circ )

( mangle b = 3x^circ )

1. ( mangle a = (7x - 3)^circ )

( mangle b = (x - 1)^circ )

1. ( mangle a = (11x + 2)^circ )

( mangle b = (8x + 7)^circ )

1. ( mangle a = (13x + 10)^circ )

( mangle b = (12x + 20)^circ )

Explanation:

Problem 32

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

\(m\angle A + m\angle B = 180^\circ\), so \(x + 3x = 180\)

Step2: Solve for \(x\)

\(4x = 180\) \(\Rightarrow\) \(x = \frac{180}{4} = 45\)

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

\(m\angle A = 45^\circ\), \(m\angle B = 3\times45 = 135^\circ\)

Step1: Use supplementary angles property

\((7x - 3) + (x - 1) = 180\)

Step2: Simplify and solve for \(x\)

\(8x - 4 = 180\) \(\Rightarrow\) \(8x = 184\) \(\Rightarrow\) \(x = 23\)

Step3: Calculate angle measures

\(m\angle A = 7\times23 - 3 = 158^\circ\), \(m\angle B = 23 - 1 = 22^\circ\)

Step1: Apply supplementary angles rule

\((11x + 2) + (8x + 7) = 180\)

Step2: Solve for \(x\)

\(19x + 9 = 180\) \(\Rightarrow\) \(19x = 171\) \(\Rightarrow\) \(x = 9\)

Step3: Find angle measures

\(m\angle A = 11\times9 + 2 = 101^\circ\), \(m\angle B = 8\times9 + 7 = 79^\circ\)

Answer:

\(m\angle A = 45^\circ\), \(m\angle B = 135^\circ\)

Problem 33