Question

two lines meet at a point that is also the endpoint of two rays. setup and solve the appropriate equations to solve for the values of angles x and y. show the steps you followed to find the unknown angles.

Answer 1

Answer:

Step-by-step explanation:

Check attachment for labeling,

To find x,

Since angle on a straight line is 180°,

Then, AOE is a straight line

<AOE = 180°

NOTE: <AOC is a right angle,

Then, <AOC = 90°

So,

<AOE = <AOC + <COE

180 = 90 + <COE

<COE = 180-90

<COE = 90°

Then, <COE is made of two angles

<COD = 71° and <DOE = x

<COE = <COD + <DOE

90 = 71 + x

x = 90 - 71

x = 19°

Also, to find y

NOTE: BOF is a straight line and angle on a straight line is 180°

<BOF = <BOC + <COD + <DOE + <EOF

180 = 37 + 71 + x + y

180 = 108 + 19 + y

180 = 127 + y

Then, subtract 127 from both sides

y = 180 - 127

y = 53°

So, x = 19° and y = 53°

Answer 2

Answer:

x = 19°

y = 53°

Step-by-step explanation:

First we can find the value of x, then the value of y.

For x, we can observe from the figure that x is complementary to the angle of 71°, that is, they both summed have 90°.

So, we have that:

x + 71 = 90

x = 19°

Now we can solve for y.

From the figure we have that y is supplementary to the angle (37° + 71° + x°), that is, they summed form a angle of 180°.

So we have that:

y + 37 + 71 + 19 = 180

y = 180 - 37 - 71 - 19 = 53°