Question

1. ∠r and ∠s are complementary angles. if the m∠r = 12x - 3 and m∠s = 7x - 2, find m∠r.
2. ∠1 and ∠2 form a linear pair. the measure of ∠2 is six more than twice the measure of ∠1. find m∠2.
3. if uw bisects ∠tuv, m∠tuw = 13x - 5

Explanation:

Step1: Use the property of complementary angles

Complementary angles sum to \(90^{\circ}\). So, \(m\angle R + m\angle S=90\). Substitute \(m\angle R = 12x - 3\) and \(m\angle S = 7x - 2\) into the equation: \((12x - 3)+(7x - 2)=90\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(12x+7x-3 - 2=90\), which gives \(19x-5 = 90\).

Step3: Solve for \(x\)

Add \(5\) to both sides: \(19x=90 + 5=95\). Then divide both sides by \(19\): \(x=\frac{95}{19}=5\).

Step4: Find \(m\angle R\)

Substitute \(x = 5\) into \(m\angle R=12x - 3\). So, \(m\angle R=12\times5-3=60 - 3=57\).

Answer:

\(57\)