Final answer:
One angle of the triangle measures 10 degrees more than the second one is x + 10 degrees. (option c)
Step-by-step explanation:
Let's denote the second angle in the triangle as x degrees. According to the given information, the first angle is 10 degrees more than the second angle. Therefore, the first angle is x+10 degrees.
The sum of the interior angles in a triangle is always 180 degrees.
Therefore, the third angle in the triangle can be found by subtracting the sum of the first two angles from 180:
x+(x+10)+Third Angle= 180
Combine like terms:
2x+10+Third Angle= 180
Subtract 10 from both sides:
2x+Third Angle= 170
Subtract 2x from both sides:
Third Angle= 170 -2x
Now, we know that the third angle is 170 -2x degrees. Since it's given that one angle is 10 degrees more than the second one, we can set up an equation:
170 -2x= x+10
Combine like terms:
170= 3x+10
Subtract 10 from both sides:
160= 3x
x= 160/3
The angles in the triangle are:
First Angle: x+10 = 160/3 + 10 degrees
Second angle: x= 160/3 degrees
Third angle: 170 -2x = 120 - 320/3 degrees
Given the answer choices, the closest representation x + 10, & therefore the final answer is c) x + 10 degrees