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3 years ago

Point Y is in the interior of ∠XWZ. Given that WX→ and WZ→ are are opposite rays, and m∠XWY=4(m∠YWZ) is m∠YWZ?.

Mathematics

1 answer:

EleoNora [17]3 years ago

5 0

Answer:

m∠YWZ=36°

Step-by-step explanation:

Opposite rays are two rays that both start from a common point and go off in exactly opposite directions. Because of this the two rays (WX and WZ) form a single straight line through the common endpoint W.

If rays WX and WZ are opposite, then angle XWZ is straight angle. A straight angle always has the measure of 180°.

Point Y is in the interior of ∠XWZ, then angles XWY and EWZ are supplementary angles (together form straight angle XWZ). Supplementary angles always add up to 180°, then

m∠XWY+m∠YWZ=180°

You are given that

m∠XWY=4(m∠YWZ).

Substitute it into the previous equality:

4(m∠YWZ)+m\angle YWZ=180°

5(m∠YWZ)=180°

m∠YWZ=36°

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Your Turn: Find the measure of angle P below. Show your work. *

Virty [35]

Check the picture.

The figure shows lines m, n and the line through points A And B, call it $l_{AB}$ .

1. The angles ABC and CBP are "supplementary" angles, that is angles whose sum is 180°, because together they form one straight angle.

thus,

(2x+5°)+(7x-14°)=180°

9x-9°=180°

9x=189°

x=189°/9=21°.

2. Remark, m and n are parallel, otherwise we can say nothing about the measure of angle P

check the second picture, notice the F shape formed by CBP and P.

Angles CBP and P are called "angles F" or "corresponding angles".

Corresponding angles formed by a line cutting 2 parallel lines, are always congruent (that is equal) so:

m(P)=m(CBP)=7x-14°=7.21°-14°=147°-14°=133°

Answer: 133°

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3 years ago

Read 2 more answers

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lutik1710 [3]

Answer:

Yes is a solution

Step-by-step explanation:

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Three friends go to the local framers market. Latasha spends $3.35. Helen spends 4 times as much as Latasha. Dee spends $7.50 mo

mylen [45]

Given:

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Helen spends 4 times as much as Latasha.

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Solution:

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miskamm [114]

Simple...

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