MHB Finding the Measures of Angles in a Linear Pair

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In a linear pair, the measures of two angles sum to 180 degrees. Given m<1 = 5x + 9 and m<2 = 3x + 11, the equation to solve is 5x + 9 + 3x + 11 = 180. Solving for x allows for the determination of the individual angle measures. Understanding the concept of a linear pair is crucial for setting up the equation correctly. The problem emphasizes the importance of recognizing angle relationships in geometry.
bernardl
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<1 and <2 form a linear pair. If m<1 = 5x + 9 and m<2 = 3x + 11, find the measures of both angles.
 
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Hi bernardl and welcome to MHB! :D

I've re-titled your recent threads to give them a name that accurately reflects the problem at hand.

A linear pair of angles have measures that sum to 180 degrees, so we want to solve

5x + 9 + 3x + 11 = 180

for x, then substitute that value for x into the respective expressions to find the measure of the two angles.
 
Whoever gave you this problem clearly expected you to know what "linear pair of angles" meant! Did you? If so it is easy to set up an equation to solve.
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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