Question

If the angle measures of a triangle can be expressed as 4x + 6, 7x - 14, and 48 - x, what is the value of the smallest angle measure? a) 14 degrees b) 34 degrees c) 62 degrees d) 84 degrees

Answer 1

To find the smallest angle, we must first find the values for all angles, which involve finding the value of x.

We know that the sum of all angles in a triangle is equal to 180 degrees. So we can write and solve an equation like this:

4x + 6 + 7x - 14 + 48 - x = 180

Simplify this to:

10x + 40 = 180

Upon further simplification, we subtract 40 from each side to give:

10x = 140

Now, we can find x by dividing both sides by 10:

x = 14

We then substitute x = 14 back into the original angle expressions:

4x + 6 => 4(14) + 6 => 56 + 6 = 62 degrees
7x - 14 => 7(14) - 14 => 98 - 14 = 84 degrees
48 - x => 48 - 14 => 34 degrees

So, the three angles of the triangle are 62 degrees, 84 degrees and 34 degrees. The smallest angle is 34 degrees.

Therefore, the answer is:
b) 34 degrees