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2 years ago

In the figure shown, t ∥ x and k ∥ w. If m∠3 = 20, list all the angles that are 20° and all the angles that are 160°.

Mathematics

1 answer:

lara [203]2 years ago

3 0

Answer:

m∠1 = m∠3 = m∠5 = m∠7 = m∠9 = m∠11 = m∠14 = m∠16 = 20°

m∠2 = m∠4 = m∠6 = m∠8 = m∠10 = m∠12 = m∠13 = m∠15 = 160°

Step-by-step explanation:

m∠3 = m∠1 = 20° {vertical angles]

m∠3 = m∠14 = m∠7 = 20° [Corresponding angles]

m∠3 + m∠6 = 180° [Consecutive interior angles]

m∠6 = 180 - 20 = 160°

m∠2 + m∠3 = 180° [Supplementary angles]

m∠2 = 180 - 20 = 160°

m∠4 = m∠2 = 160° [Vertical angles]

m∠2 = m∠6 = m∠10 = m∠15 = 160° [Corresponding angles]

m∠7 = m∠9 = 20° [Corresponding angles]

m∠10 = m∠12 = 160° [Vertical angles]

m∠12 = m∠13 = 160° [Corresponding angles]

m∠1 = m∠5 = m∠16 = 20° [Corresponding angles]

m∠14 = m∠16 = 20° [Vertical angles]

m∠13 = m∠15 = 160° [Vertical angles]

Therefore, m∠1 = m∠3 = m∠5 = m∠7 = m∠9 = m∠11 = m∠14 = m∠16 = 20°

m∠2 = m∠4 = m∠6 = m∠8 = m∠10 = m∠12 = m∠13 = m∠15 = 160°

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