Question

a transversal crosses parallel lines creating corresponding angles r and t.

• (mangle r=(15.5x)^{circ})
• (mangle t=(3.2x + 98.4)^{circ})

what is (mangle r)?
a. (124.0^{circ})
b. (68.2^{circ})
c. (102.3^{circ})
d. (117.1^{circ})

Explanation:

Step1: Use corresponding - angles property

Since corresponding angles formed by a transversal crossing parallel lines are equal, we set \(m\angle R=m\angle T\). So, \(15.5x = 3.2x+98.4\).

Step2: Solve the equation for \(x\)

Subtract \(3.2x\) from both sides: \(15.5x - 3.2x=3.2x + 98.4-3.2x\), which simplifies to \(12.3x=98.4\). Then divide both sides by \(12.3\): \(x=\frac{98.4}{12.3}=8\).

Step3: Find \(m\angle R\)

Substitute \(x = 8\) into the expression for \(m\angle R\). \(m\angle R=15.5x\), so \(m\angle R=15.5\times8 = 124^{\circ}\).

Answer:

A. \(124.0^{\circ}\)