Question

In a triangle, the second angle measures twice the first. The measure of the third angleis 24° more than the first. Find the measures of the three angles.Use X in the equation

Answer 1

Assume the first angle measures X degrees

First angle = X

The second angle measures twice the first, thus

Second angle = 2X

The third angle is 24° more than the first, that is

Third angle = X + 24

The sum of the angles in any triangle must be 180°, thus

X + 2X + X + 24 = 180

Joining like terms

4X + 24 = 180

Subtracting 24 in both sides of the equation

4X = 180 - 24 = 156

Solving for X

X = 156 / 4 = 39

Now we know the first angle is 39°

Second angle = 2X = 78°

Third angle = X + 24 = 39 + 24 = 63°

Let's check:

39° + 78° + 63° = 180°