Question

enter the given angle measure int diagram.
given:
oz bisects ∠roc.
m∠hoj = 25°.
enter the measures and reasons to justify each step needed
to calculate m∠roc.
m∠roc =
diagram notes:

Explanation:

Step1: Use vertical angles property

Vertical angles are equal. Since \(m\angle HOJ = 25^{\circ}\), and \(\angle ZOC\) and \(\angle HOJ\) are vertical angles, so \(m\angle ZOC=25^{\circ}\)

Step2: Use angle - bisector definition

Given \(OZ\) bisects \(\angle ROC\), by the definition of an angle bisector \(\angle ROZ=\angle ZOC\). So \(m\angle ROZ = 25^{\circ}\)

Step3: Calculate \(m\angle ROC\)

By the angle - addition postulate \(m\angle ROC=m\angle ROZ + m\angle ZOC\). Substitute \(m\angle ROZ = 25^{\circ}\) and \(m\angle ZOC=25^{\circ}\) into the formula: \(m\angle ROC=25^{\circ}+25^{\circ}\)

Answer:

\(50\)