Question

find the measures of the indicated angles, using the diagram below. given a=(9x)° and d=(10x - 14)°, find the measures of a and d.

Explanation:

Step1: Identify angle - relationship

Since \(m\parallel n\), angles \(A\) and \(D\) are vertical angles. Vertical angles are equal. So, \(A = D\).

Step2: Set up the equation

Set \(9x=10x - 14\).

Step3: Solve the equation for \(x\)

Subtract \(9x\) from both sides: \(0 = 10x-9x - 14\), which simplifies to \(x = 14\).

Step4: Find the measure of angle \(A\)

Substitute \(x = 14\) into the expression for \(A\). \(A=9x\), so \(A = 9\times14=126^{\circ}\).

Step5: Find the measure of angle \(D\)

Since \(D = A\), \(D=126^{\circ}\) (or substitute \(x = 14\) into \(D = 10x - 14\): \(D=10\times14 - 14=140 - 14 = 126^{\circ}\)).

Answer:

\(A = 126^{\circ}\), \(D = 126^{\circ}\)