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One angle of the triangle measures 10 degrees more than the second one.

a) x degrees
b) x + 5 degrees
c) x + 10 degrees
d) x - 10 degrees

User Nurieta
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1 Answer

1 vote

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

User Wolfish
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