Chapter 6.1, Problem 32P

The measure of one of the angles of a triangle is 35. The sum of the measures of the other two angles is 145 and the difference between their measures is 15. What are the measures of the unknown angles?

To determine

To find: The measures of the unknown angles of a triangle.

Answer to Problem 32P

The measures of unknown angles are 80 and 65.

Explanation of Solution

Given information: The measure of one angle of a triangle is 35. The sum of measures of other two angles is 145. The difference between their measures is 15.

Formula used: Solve the system of equations using elimination method.

Calculation:

Letunknown angles are x and y .

The sum of interior angles of a triangle is ${180}^{\circ }$

  $x+y=145$ -----(1)

The difference between the angle measures is 15.

Equation for this is

  $x-y=15$ -------(2)

Solve the two equations using elimination method.

Add the equations to eliminate the y terms.

  $\begin{array}{l}x+y=145\\ x-y=15\\ --------\\ 2x=160\end{array}$

Divide both sides by 2.

  $x=80$

Substitute x as 80 into any of the equations to find y .

  $80+y=145$

Subtract both sides 80

  $y=65$

Conclusion: Hence the unknown angles are 80 and 65.