Find measure of each angle

Question

The measure of the largest angle of a triangle is three less than five times the measure of the smallest angle. The measure of the remaining angle is one less than twice the measure of the smallest angle. Find the measure of each angle.

Answer 1

The sum of the three angles in any triangle is 180 degrees.

 

Set the variables for each angle.

 

Let the smallest angle = x

Let the second smallest angle = 2x - 1

Let the largest angle = 5x - 3

 

 

Set up the equation.

 

x + (2x - 1) + (5x - 3) = 180

 

 

Solve for x.

 

8x - 4 = 180

 

 

Add 4 on both sides of the equation.

 

8x = 184

 

 

Divide by 8 on both sides of equation.

 

x = 23

 

 

Substitute this value of x into the variables we set up earlier to find the angles.  I leave this part to you.