Question

The two smallest interior angles in a right triangle have measures of (2m) degrees and (2m-6) degrees. What is the value of m?

a) m = 36
b) m = 24
c) m = 18
d) m = 12

Answer 1

In a right triangle, the sum of the two smaller interior angles is always equal to 90 degrees, as the right angle itself is 90 degrees.

So, you can set up an equation:

(2m) + (2m - 6) = 90

Combine like terms:

4m - 6 = 90

Now, isolate m:

\4m = 96

\m = 24

Therefore, the correct answer is:

b) (m = 24)

Answer 2

To find the value of m in the right triangle with interior angles expressed as (2m) and (2m-6) degrees, set up the equation 2m + (2m - 6) = 90 and solve for m. The result is m = 24.

Step-by-step explanation:

The question involves calculating the value of m in a right triangle where the two smallest interior angles are given by the expressions (2m) degrees and (2m-6) degrees. In a right triangle, the sum of the two non-right angles must be 90 degrees as the right angle accounts for the other 90 degrees of the 180 degrees in any triangle. Therefore, setting up an equation 2m + (2m - 6) = 90 will help us find the value of m.

Combining like terms gives us 4m - 6 = 90. Adding 6 to both sides of the equation gives us 4m = 96. Dividing both sides by 4 gives us m = 24, which is the value of m.