What is m∠2 + m∠3? Explain. Two lines and two line segments. Lines A B and C D are parallel horizontal lines with point C directly below point A and point D directly below point D. A vertical segment extends from A to C. A diagonal segment extends from C to B. Angle B A C is labeled 1. Angle A C B is labeled 3. Angle B C D is labeled 4. Angle A B C is labeled 2. A. 180; m∠1 + 90 = 180, so m∠2 + m∠3 = 180. B. 180; m∠1 + 90 = m∠2 + m∠3, so m∠2 + m∠3 = 180. C. 90; m∠1 + m∠2 + m∠3 = 180. m∠1 = 90, so m∠2 + m∠3 = 90. D. 90; ∠2 and ∠3 are corresponding angles, so m∠2 + m∠3 = 90.

Answers

Answer 1

The line AB and the segments AC and BC form triangle ∆ABC, which gives the measure of m‹2 + m‹3 as following option;

C. 90°; m‹1 + m‹2 + m‹3 = 180°. m‹1 = 90°, so m‹2 + m‹3 = 90°

How can m‹2 + m‹3 in ∆ABC be calculated?

From the given descriptions, we have;

Lines AB and CD are horizontal lines.

Segment that extends from A to C which is segment AC is a vertical line

Therefore;

m‹BAC = m‹1 = 90°

‹BAC, ‹ABC, and ‹ACB, which are angles 1, 2, and 3 are interior angles of ∆ABC

Which gives;

m‹1 + m‹2 + m‹3 = 180° (sum of interior angles of a triangle theorem)

Therefore;

90° + m‹2 + m‹3 = 180° (substitution property)

m‹2 + m‹3 = 180° - 90° = 90°

m‹2 + m‹3 = 90°

The correct option is therefore;

C. 90°; m‹1 + m‹2 + m‹3 = 180°. m‹1 = 90°, so m‹2 + m‹3 = 90°

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Answer 2

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