 Mathematics
28 March, 11:06

# two angles of a triangle have equal measures for the third angles measure is 36 degrees less than the sum of the other two find the measure of each angle of the triangle the first and second angles measure blank degrees and the third angle measures blank degrees

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Answers (1)
1. 28 March, 12:59
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Answer: The first and second angles measure 54 degrees each. The third angle measures 72 degrees.

Step-by-step explanation:

First, I transcribed the sentences into equations.

The first part of the sentence says that "two angles of a triangle have equal measures", and we can use the konwledge that the interioir angle sum of all triangles in 180 degrees to solve this.

Lets call the first and second angles x and the third angle y. Then we can get the equation that 2x + y = 180. You might be asking "where did the 2x come from?", well, we know that if we add all of the angles up we get 180 degrees, and since two of the angles are equal, they can be simplified to 2x.

The second part of the sentence says that "the third angles measure is 36 degrees less than the sum of the other two", which translates to:

y = 2x - 36

Then we can substitute the second equation into the first and solve!

2x + (2x - 36) = 180

4x - 36 = 180

4x = 216

x = 54

Knowing that x = 54, we can substitute back into the first equation to solve for y. 2 (54) + y = 180, 108 + y = 180, y = 72.
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