Two angles of the triangle have given measures. Find the measure of the third angle
x degrees, 120 degrees minus x degrees
The angles of a triangle add up to 180°.
x + (120-x) + third angle = 180°
third angle = 180° - x - (120-x)
= 180° - 120°
= 60°
To find the measure of the third angle of a triangle, we need to know that the sum of all three angles of a triangle is always 180 degrees.
Let's solve for the third angle using the given information:
The measures of the two given angles are x degrees and 120 degrees minus x degrees.
The sum of the three angles is x degrees + (120 degrees - x degrees) + third angle.
This sum should be equal to 180 degrees.
So, we can write the equation:
x + (120 - x) + third angle = 180.
Simplifying the equation:
120 + third angle = 180.
To isolate the third angle, subtract 120 from both sides:
third angle = 180 - 120
third angle = 60 degrees.
Therefore, the measure of the third angle is 60 degrees.