Question

find the measure of angles a, b, c, and d.15°17°part 1 of 4m∠a=12°

Explanation:

Step1: Use vertical angles property

Vertical angles are equal. Angle \(a\) and the angle composed of \(15^{\circ}\) and \(17^{\circ}\) are vertical angles.
\(m\angle a=15^{\circ}+ 17^{\circ}\)

Step2: Calculate \(m\angle a\)

\(m\angle a = 32^{\circ}\)

Step3: Use vertical angles property for \(m\angle c\)

\(m\angle c=15^{\circ}\) (vertical angles with the \(15^{\circ}\) angle)

Step4: Use vertical angles property for \(m\angle d\)

\(m\angle d = 17^{\circ}\) (vertical angles with the \(17^{\circ}\) angle)

Step5: Use vertical angles property for \(m\angle b\)

Since \(m\angle a = 32^{\circ}\), and \(m\angle b\) is vertical - opposite to the angle composed of \(15^{\circ}\) and \(17^{\circ}\) (same as \(a\)'s relation), \(m\angle b=32^{\circ}\)

Answer:

\(m\angle a = 32^{\circ}\), \(m\angle b=32^{\circ}\), \(m\angle c = 15^{\circ}\), \(m\angle d=17^{\circ}\)