Solve algebraically using the system of three equations Begi

Solve algebraically using the system of three equations. Begin by introducing variables together with the units of measure (not optional!), then write the system of equtions and solve.

2) The measure of the largest angle of a triangle is 80 degrees more than the measure of the smallest angle, and the measure of the remaining angle is 10 degrees more than the measure of the smallest angle. Find the measure of each angle.

Solution

Let the three angles of triangle be A, B, C

A ---largest ; C ----> smallest

measure of the largest angle of a triangle is 80 degrees more than the measure of the smallest angle

A = C+80 -----(1)

A -C = 80

measure of the remaining angle is 10 degrees more than the measure of the smallest angle.

B = C+10 ----(2)

C -B = -10

Sum of three angles of a triangle = 180

A+B+C = 180 -----(3)

Solve equations 1, 2 and 3

Add all the euqtaions and substitute from equation 2 to solve for A, B and C

we get A = 110 deg

B = 40 deg

C = 30 deg