CONCEPT PREVIEW In each figure, find the measures of the numbe...

Question

CONCEPT PREVIEW In each figure, find the measures of the numbered angles, given that lines m and n are parallel.

Accepted Answer

Hello, everyone. We are given a figure and the lines P and Q are parallel, we are asked to find the angles denoted by the numerals. So in our figure, we have two parallel lines P and Q, they are cut by a transversal. And we are told that the top left angle is 149 degrees continuing clockwise around the first intersection. The angle on the top right is one bottom, right is three, bottom left is two. Were the transversal intersects with line Q? We have going clockwise from the top right 576 and four. We want to find the value of all of those angles. There are multiple ways to do this. So we'll go through them one at a time. I'm going to list all of my angle numbers down. So I have angle one, angle two and goes three, angle four, angle five, angle six and angle seven just so I have all of the answers in one place. So the first one that jumps at me is angle three because angle three in our given angle of 149 degrees are vertical angles, vertical angles are equal. So this means that angle three must be 149 degrees. And again, that's because it's a vertical angle from there. I want to find what is the measure of angle one. So angle one is supplementary with our given angle. So this means angle one is 180 degrees minus 149 degrees. So angle one would have to be 31 degrees. And again, this was because these were supplementary. Angle two is a vertical angle with angle one and vertical angles are equal. So angle two must also be 31 degrees. And like I said, there's multiple ways of finding this. This is just the way that makes most sense to me. Next, I'm gonna find angle five because I recall that same sided interior angles are supplementary. So if they're supplementary, this means angle three and angle five add up to 180 degrees. So 180 degrees minus 149 degrees is 31 degrees. Again, so angle five would be 31 degrees. Again, I'm using with the definition of supplementary angles from there. Angle six is a vertical angle to angle five. So they would be equal. So angle six is 31 degrees. Also, again, I'm using vertical angles. Now I need to find angles four and seven. And again, there are many ways to do this. I'm gonna use the fact that corresponding angles are equal because angle four corresponds with the given angle 149 degrees. So angle four is also 149 degrees. Angle seven is a vertical angle with angle four. So angle seven must also be 149 degrees. So in the end, we have angle one is 31 degrees. Angle two is 31 degrees. Angle three is 149 degrees. Angle four is 149 degrees. Angle five is 31 degrees. Angle six is 31 degrees. Angle seven is 149 degrees. Have a nice day.

CONCEPT PREVIEW In each figure, find the measures of the numbered angles, given that lines m and n are parallel.

Key Concepts

Parallel Lines and Transversals

Angle Relationships

Properties of Supplementary and Complementary Angles

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