UNIT 5 SIMILARITY, RIGHT TRIANGLE TRIGONOMETRY, AND PROOF
Lesson 5: Proving Theorems About Lines and Angles
In the diagram that follows, AC and BD intersect. Use this information to see for the measures
the unknown angles in problems 5 and 6. Show and justify your work.
N
5. Find m24 if mZ2=3x +74 and
23=2x+11.
6. Find m23 if mZ1=112-9 and
23=7r+23.

M4 and m2 are equivalent
M2 and m3 are supplementary angles which mean they add up to 180°

M2+m3=180

Plug in the equation
3x+74+2x+11=180
Add up the x’s 3x+2x=5x
Add the constants on the left side
74+11=85
You get 5x+85=180
Subtract 85 from both sides
5x=95
Divide by 5
X=19

Now plug x into the m3 equation and get
2*19+11=49°
Because m4=m3, m4=49°

M3 and m1 are equivalent so set both equations equal to each other and solve bringing the same variables on each side

11x-9=7x+23
11x-7x=23+9
4x=32
X=8

Now plug x into either equation and you get
M3=79°