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Lesson 4: Missing angle problems

# Find measure of angles word problem

Solve this word problem to find the measure of angles. In this example you'll split up a pie (don't forget to share!). Created by Sal Khan.

## Want to join the conversation?

• It seems like an equally valid answer would be that you cut yourself a 20 degree slice, and cut your brother a 10 degree slice. Where did the idea come from that these 3 slices would consume the entire remains of the pie?
• In fact, you're right. For it to be an exam question, it must be clearer.
• Couldn't you just do 180-30=150, then divide 150 by 3 which equals 50, and then multiply 50 times 2 to get 100? Wouldn't that be a lot simpler?
• yes but this strategy would only be valid with this specified problem
• I don't get any of this -_-
• Unfortunately, that is why we are here. to learn things like (9-4x) -2 (4y+8) +83y= -18x (14-13) -9x
• I feel like bad for the mom in this situation. She gets such a tiny amount. couldn't you just split it into 3 equal slices? Your slice isn't even a slice, it's like 2 slices. lol
• Two angles are supplementary. The measure of the larger angle is
10 degrees more than the product of 4 and the measure of the smaller angle.
What is the measure of the larger angle in degrees?
• Let's call larger angle "x" and the smaller angle "y".
We can use the given information to create a system of equations:
x + y = 180 (this is because they are supplementary)
x = 4y + 10 (The measure of the larger angle is 10 degrees more than the product of 4 and the measure of the smaller angle.)
Solving this system:
4y + y + 10 = 180
5y + 10 = 180
5y = 170
y = 34˚
x + 34 = 180
x = 146˚
• My brother: Can I have some pie?
Me: Ok here you go
*Proceeds to give him π*
• Another way to write the equation that directly answers the question is to let x be the amount that you eat and write:
x+1/2x+30=180 (your brother's pie is half of yours) simplify---> 1.5x+30=180 and solve for x. This will give you the answer 100, without doing the extra step outside of the equation of multiplying by 2 to find the final answer. (ie, instead of x is your brother's pie, and 2 times x is your slice of pie.)