<u>Question: In a triangle, the measure of the first angle is three times the measure of the second angle. The measure of the third angle is 70 degrees more than the measure of the second angle. Use the fact that the sum of the measures of the three angles of a triangle is 180 degrees to find the measure of each angle.
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<u>The measure of the first angle is </u>
<u>_________degrees.
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<u>The measure of the second angle is </u>
<u>___________degrees.
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<u>The measure of the third angle is </u>
<u>_____degrees.</u>
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Answer: Since we know that a triangle equals 180 degrees, we can set up an equation with the following unknown numbers and the known degrees for the measure of angle 3.
We know that the measure of angle one is 3 times the number of the measure of angle 2, we can represent that as 3x.
The first angle of the triangle can be seen as 3x
The third angle can be represented by 70 more than the measure of angle two.
The second angle can be represented by x. Since we don't know the value.
The following equation is 3x+x+x+70=180
We have to put it equals 180 because a triangle equals 180.
We first combine like terms and get 5x+70=180
Then we subtract 70 to both sides to get x by itself. Then we get
5x=110
We solve for x and then get 22, this is the measure for the second angle.
So now that we know the measure of the second angle, we know that the measure of the first angle is 3 times more than the second angle, so we have to multiply 22 by 3 to get the measure of the second angle.
We get 66 degrees for the first angle.
Lastly, to get the measure of the second angle, we have to add 22 to 70 to get the last angle. This will leave us of with
66+22+22+70; which equals 180; which is a triangle:)
REAL ANSWERS:
The measure of the first angle is 66 degrees.
The measure of the second angle is 22 degrees.
The measure of the third angle is 92 degrees.
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