measures of angles

Question

In a triangle, the measure of the first angle is twice the measure of the second angle. The measure of the third angle is 96 more than the measure of the second angle . Use the fact of the sum of the measure of the three angle of a triangle are 180 to find the measure of each angle.

Answer 1

let x = measure of first angle;  let y = measure of second angle;  let z = measure of third angle;

 

then:  x = 2y;  z = y + 96;   and x + y + z = 180 ---> 2y + y + y + 96 = 180 ---> 4y + 96 = 180 ---> 4y = 180 - 96

 

---> 4y = 84 ---> y = 21 ---> x = 2(21) = 42;  z = y + 96 = 21 + 96 --->  z = 117

 

check: x + y + z = 42 + 21 + 117 = 63 + 117 = 180 (check)