Question

Math questionCharlie tells Tony that in a triangle none of the angles are known. However, the largest angle is 5 more than double the smallest angle, the middle angle is 10 less than double the smallest angle. What are the measurments of each angle? Labled Diagram needed and full solution using algebra.

Answer 1

37, 64, and 79 degrees.

Step-by-step explanation:

Let's call x, y, and z the measures of the angles in the triangle, where x is the smallest angle and z is the largest angle.

The sum of the interior angles of a triangle is always equal to 180 degrees, so we can write the following equation:

x + y + z = 180

Then, the largest angle z is 5 more than double the smallest angle x, so:

z = 5 + 2x

And the middle angle y is 10 less than double the smallest angles:

y = 2x - 10

Now, we can replace the last equations on the first one to get:

x + y + z = 180

x + (2x - 10) + (5 + 2x) = 180

Solving for x, we get:

x + 2x - 10 + 5 + 2x = 180

5x - 5 = 180

5x - 5 + 5 = 180 + 5

5x = 185

5x/5 = 185/5

x = 37

So, the value of the smallest angle is 37.

Now, we can calculate the value of the other angles as:

y = 2x - 10

y = 2(37) - 10

y = 74 - 10

y = 64

z = 5 + 2x

z = 5 + 2(37)

z = 5 + 74

z = 79

Therefore, the measurements of the angles are 37, 64, and 79 degrees.