Question

enter the given angle measure into the diagram.
given:

• oi bisects ∠doc.
• m∠doi = 50°

enter the measures and reasons to justify each step needed to calculate m∠cor.
m∠cor =
diagram notes:
first enter the given information for ∠doi

Explanation:

Step1: Use the angle - bisector definition

Since \(OI\) bisects \(\angle DOC\), by the definition of an angle bisector, \(\angle DOI=\angle COI\). Given \(\angle DOI = 50^{\circ}\), so \(\angle COI=50^{\circ}\).

Step2: Use the straight - angle property

\(\angle ROC+\angle COI+\angle DOI = 180^{\circ}\) (because \(R\), \(O\), and \(L\) are collinear, and the sum of angles on a straight line is \(180^{\circ}\)). Let \(m\angle ROC=x\). Then \(x + 50^{\circ}+50^{\circ}=180^{\circ}\).

Step3: Solve the equation for \(x\)

$$
LATEXBLOCK0
$$

Answer:

\(80\)