Question

enter the given angle measure into the diagram.
given:

• \\( \angle m o h \cong \angle r o b \\).
• \\( m \angle r o b = 50 ^ { \circ } \\).
• \\( m \angle h o b = 75 ^ { \circ } \\).

enter each measure required to calculate \\( m \angle m o b \\), starting
with the given information.

• the measure of \\( \angle m o b \\) can be calculated.

\\( m \angle m o b = \\)

• the measure of \\( \angle m o b \\) can not be calculated.

diagram notes:

Explanation:

Step1: Use the property of congruent angles

Since \(\angle MOH\cong\angle ROB\), then \(m\angle MOH = m\angle ROB=50^{\circ}\)

Step2: Use the angle - addition formula

We know that \(\angle MOB=\angle MOH+\angle HOB\) (by the angle - addition postulate: if \(O\) is a point in the interior of \(\angle MOB\), then \(m\angle MOB = m\angle MOH+m\angle HOB\))
Substitute \(m\angle MOH = 50^{\circ}\) and \(m\angle HOB=75^{\circ}\) into the formula: \(m\angle MOB=50^{\circ}+75^{\circ}\)

Answer:

\(125\)