Two angles of a triangle have the same measure and the third one is 6 degrees greater than the measure of each of the other two. Find the measure of the LARGEST angle in the triangle.
Answers
Answer:
Step-by-step explanation:
So we have two angles that measure the same. Let each angle be X. The third angle is 39 degrees greater than the measure of each of the other two. This means the third angle is x+39 degrees. From this we can write a formula:
x+x+x+39=180 degrees. (The sum of the angles of a triangle is 180.)
Combine like terms:
3x+39=180
Solve for X
3x+39-39=180-39
3x=141
3x÷3=141÷3
x=47
The largest angle equals 47+39=86.
Now lets check it 47+47+86=180.
The value of the largest angle is 64 degrees.
GIVEN: Two angles of a triangle have the same measure and the third one is 6 degrees greater than the measure of each of the other two.
TO FIND: Measure of greatest angle
SOLUTION:
As we are given in the question,
Two of the angles are the same.
Therefore,
Let the first angle be x.
Implying that,
The second angle will also be x.
Also,
According to the question,
The third angle will be x + 6.
Now,
Using the angle sum property,
x+x+x+6 = 180 degrees. (The sum of the angles of a triangle is 180.)
Combine like terms:
3x+6=180
Solve for X
3x = 180 - 6
3x = 174
x = 174/3
x = 58
Therefore,
The largest angle equals 58 + 6 = 64.
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