Question

Three rays have a common vertex on a line. Show all of your work and explain, using math evidence, the measures of m and n. (Make sure to use the C-E-R strategy to respond: Make your CLAIM; use words from the question to answer the question being asked; state what you discovered from your math EVIDENCE and facts; and REASONING. 221 62 27"​

Answer 1

• m° = 63°
• n° = 28°

Explanation:

You want the measures of the angles marked m° and n° in the given figure.

CER model

The Claim, Evidence, Reasoning (CER) model tells us an explanation consists of:

• A claim that answers the question.
• Evidence from given data.
• Reasoning that describes why the evidence supports the claim

Angle m

Claim: The measure of m° is 63°.

Evidence: Angle m° is one of three angles in the figure that form a straight angle.

Reasoning: The measure of a straight angle is 180° (definition). The sum of the angles is equal to the whole (angle addition theorem).

m° +90° +27° = 180°

m° = 63° . . . . add -117° to both sides (addition property of equality)

Angle n

Claim: The measure of n° is 28°.

Evidence: Angle n° is one of two angles in the figure that form a right angle.

Reasoning: The square corner signifies a right angle, whose measure is 90°. The angle addition theorem tells us that angle is the sum of the two angles into which it is divided:

90° = 62° + n°

28° = n° . . . . . . . add -62° to both sides (addition property of equality)