To find the number of degrees in the greatest angle of the triangle when its measure equals the sum of the measures of the other two angles, we can set up an equation based on the properties of the angles of a triangle.
Let's denote the greatest angle as A, and the other two angles as B and C. According to the problem statement, the greatest angle A is equal to the sum of the other two angles, so we have:
A = B + C
We know that the sum of the angles in any triangle is always 180 degrees. Therefore, we can write the following equation to represent the sum of the angles of the triangle:
A + B + C = 180 degrees
Now, we can substitute the expression for A (from the first equation) into the second equation:
(B + C) + B + C = 180 degrees
Notice that we now have two Bs and two Cs. This simplifies to:
2B + 2C = 180 degrees
We can combine the terms on the left side by adding them:
2 * (B + C) = 180 degrees
Divide both sides by 2 to solve for the expression B + C:
B + C = 180 degrees / 2
B + C = 90 degrees
Since A is equal to the sum of B and C, and we have found that B + C equals 90 degrees:
A = 90 degrees
Therefore, the greatest angle, A, in the triangle is 90 degrees.
