Question

What are the measures of Angles a, b, and c? Show your work and explain your answers. (10 points)

Two straight lines intersect at a point to form angle a. The measure of the angle opposite to angle a is 30 degrees. Angle a is the angle of a right triangle having another angle equal to b. A triangle with one angle labeled c is on the left of the figure. The angle adjacent to c is labeled 75 degrees.

Answer 1

Okay, let's first find angle a
vertical angles are congruent, so since the opposite angle is 30 degrees, what is the angle of a?

Answer 2

I'm not sure. How do I find it?

Answer 3

They're equal, congruent... so if one is 30 degrees the opposite is....?

Answer 4

It is 30

Answer 5

yes angle A is 30

Answer 6

And since you know that all the angles in a triangle add up to 180 degrees
You can set it up to 90 degrees + angle a + angle b = 180
So you have 90 + 30 + b= 180 and then you can solve for b

Answer 7

Okay, thanks!

Answer 8

so what's angle b?

Answer 9

10

Answer 10

huh no
30 + 90 + b = 180
120 + b = 180
b is...?

Answer 11

Ohh
60

Answer 12

yes

and now angle c
a straight angle is 180 degrees so
75 + c = 180

Answer 13

105

Answer 14

yes so there you go, you have all 3 angles .-.

Answer 15

Thank you

Answer 16

yw~