Question

The first angle of a triangle is 10 degrees less than the second angle. The third angle of a triangle is two times the second angle. Use x to represent the unknown value.

Answer 1

Hi there!
Let the second angle be represented by x. Now, just use the given information to write expressions for each angle.
Angle 1:
The question says that it is 10 degrees less than the second angle. Therefore, it can be represented by the expression x - 10.
Angle 2:
Represented by x.
Angle 3:
As said in the question, the third angle is 2 times the second angle. This gives us the expression 2 × x, giving us 2x.
Now, take all the expressions and add them up and make them equal to 180 degrees, according to the Triangle Sum Theorem.
x + 2x + x - 10 = 180
4x - 10 = 180
4x = 190
/4     /4
x = 47.5
Therefore, the angle measures are 47.5 degrees, 2(47.5) = 95, and 47.5 - 10 = 37.5 degrees. Hope this helped!