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1 year ago

Use the figure to find the measures of the numbered angles. Explain your reasoning

Mathematics

1 answer:

LUCKY_DIMON [66]1 year ago

3 0

The measures of the numbered angles are as follows:

m∠1 139°
m∠2 = 41°
m∠3 = 139°
m∠4 = 139°
m∠5 = 41°
m∠6 = 139°
m∠7 = 41°

m∠1 = 117°
m∠2 = 63°
m∠3 = 117°
m∠4 = 63°
m∠5 = 117°
m∠6 = 63°
m∠7 = 63°

<h3>How to find measures of angles?</h3>

When parallel lines are cut by a transversal line, angle relationships are formed such as alternate angles, corresponding angles, linear angles, vertically opposite angles etc.

Therefore, line a and b are parallel to each other. The transversal line t cut the parallel lines.

Hence,

m∠1 = 180 - 41 = 139° (angles on a straight line)

m∠2 = 41° (vertically opposite angles)

Vertically opposite angles are congruent.

m∠3 = 139° (vertically opposite angles)

m∠4 = 180 - 41 = 139° (same interior angles)

Same interior angles are supplementary.

m∠5 = 41° (same interior angles)

m∠6 = 139° (vertically opposite angles)

m∠7 = 41° (vertically opposite angles)

m∠1 = 117° (alternate exterior angles)

Alternate exterior angles are congruent

m∠2 = 180 - 117 = 63° (sum of angles on a straight line)

m∠3 = 117° (vertically opposite angles)

m∠4 = 63° (vertically opposite angles)

m∠5 = 117° (vertically opposite angles)

m∠6 = 180 - 117 = 63° (sum of angles on a straight line)

m∠7 = 63° (vertically opposite angles)

learn more on angles here: brainly.com/question/19068435

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Answer:

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