Question

It is given that m ∠ AOB = 42 ∘ and m ∠ EOF = 66 ∘ . By the ___________, ∠ EOF ≅ ∠ BOC . Therefore, m ∠ BOC = 66 ∘ . By the ________ , m ∠ AOC = 108 ∘ , and by ________ the , m ∠ AOC + m ∠ COD = 180 ∘ . After application of the ___________, m ∠ COD = 72 ∘ .

Answer 1

The student's geometry question involves the Vertical Angle Theorem, Linear Pair Postulate, Supplementary Angles Theorem, and Subtraction Property of Equality to determine the measures of angles around a point given two angle measurements.

Step-by-step explanation:

To answer the student's question, let's fill in the blanks with the appropriate terms and justify them:

It is given that m ∠ AOB = 42 ° and m ∠ EOF = 66 °. By the Vertical Angle Theorem, ∠ EOF ≅ ∠ BOC. Therefore, m ∠ BOC = 66 °. By the Linear Pair Postulate, m ∠ AOC = 108 °, and by the Supplementary Angles Theorem, the m ∠ AOC + m ∠ COD = 180 °. After the application of the Subtraction Property of Equality, m ∠ COD = 72 °.

The Vertical Angle Theorem says that opposite angles formed by two intersecting lines are congruent. The Linear Pair Postulate states that if two angles form a linear pair (meaning they are adjacent and their non-common sides are opposite rays), then the angles are supplementary. The Supplementary Angles Theorem indicates that if two angles are supplementary, their measures add up to 180°. Lastly, the Subtraction Property of Equality allows us to subtract the same value from both sides of an equation, which is how we find the measure of ∠ COD.