# Help me find the angles?

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Jul 7, 2017
1. x= 43°; y=133°

2. x= 78°

3. x=20; y =110°

#### Explanation:

Question One:

In the annotated diagram below, we are given a right angle which you know is 90° We are also given an angle of 47°. Given this, we can say a few things that will help us find the values of $x$ and $y$

For $x$, we can see that we have a perpendicular angle with the right side already labeled for us, we can say that the right side is also 90° which means that the line segment $\overline{A B}$ is equal to 180° In addition, we have some complementary angles on the left whose sum of the angles is 90°

Therefore to find $x$ we can do this in several ways.

Say we didn't notice that we had a perpendicular angle or that the left side was equal to the right. If we only knew that the angles of line segment $\overline{A B}$ summed up to $180$ we could have used the following equation: 47°+90°+x°=180 and solve for $x$ which would have given us 43°. Another way was knowing that we had perpendicular angles which is shown in the annotated image above.

For $y$, you seemed to have realized the vertical angles which is to say...

Knowing that we are also dealing with supplementary angles whose angle sum is 180°: (See example below)

Thus, to find $y$ we can come up with an equation 47°+y°=180 and solve for $y$ or simply 180°-47° will give you the value of $y$. In either case, y°=133

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Question 2:

Again we have some vertical angles as well as a straight angle whose sum is 180° that is divided into $3$ angles. Knowing that if one vertical angle is 24°, the other one is 24° as well.

To find $x$ we can therefore come up with the equation $2 x + 24 = 180$ ($2 x$ because we have $2$ $x$'s). We solve for $x$ and find that the angles that make up the straight angle are 78°, 78° and 24°

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Question $3$:

Finally, we have this tricky one which requires you to do some algebra. We see some supplementary angles but we don't know what their angles are. Instead they are given to us in the form of an algebraic expression. Though we may not know what the angles are exactly, we do know that the sum of them will be 180° Thus we have to find $x$ by coming up with the following equation: $5 x + 45 + 3 x - 25 = 180$

Once we find $x$, we substitute it to find all the angles except y°.

To find y° you must see that $\angle C D$ or that the angles that make up the line segment $\overline{C D}$ sum up to be 180°. Therefore, y° can be found by setting up the equation: 35°+35+y°=180 or $180 - \left(35 + 35\right)$. In either case, y°=110°#

Whoo! That was a lot but I hope I helped! :)