Angles of a Triangle

Question

Angles of a triangle

 

The second angle of a triangle garden is four times as large as the first. The third angle is 45 degrees less than the sum of the other two angles. Find the measure of each angle.

Answer 1

Let the first angle = x

Let the second angle = 4x

Let the third angle = (x + 4x) - 45 = 5x - 45

 

Since the sum of the angles in a triangle is 180 degrees, we can write an equation that represents the sum of the angles using the variables.

 

x + 4x + 5x - 45 = 180

 

 

Solve for x from this equation.

 

10x - 45 = 180

 

 

Add 45 on both sides of the equation.

 

10x = 225

 

 

Divide both sides of the equation by 10.

 

x = 22.5

 

 

This is the first angle.  Substitute this value of x into the other variables to find the other two angles.