Question

The sum of the measures of the angles of a triangle is 180. The sum of the measures of the second and third angles is three times the measure of the first angle. The third angle is 15 more than the second. Let x, y, and z represent the measures of the first, second, and third angles, respectively\

Answer 1

Question:

The sum of the measures of the angles of a triangle is 180. The sum of the measures of the second and third angles is three times the measure of the first angle. The third angle is 15 more than the second. Let x, y, and z represent the measures of the first, second, and third angles, respectively. find the measure of each angle

Answer:

The measure of first angle is 45 degrees and measure of second angle is 60 degrees and measure of third angle is 75 degrees

Solution:

Let the measure of first angle be "x"

Let the measure of second angle be "y"

Let the measure of third angle be "z"

Given that,

The sum of the measures of the angles of a triangle is 180

x + y + z = 180 ---------- eqn 1

The sum of the measures of the second and third angles is three times the measure of the first angle

second angle + third angle = 3 times the first angle

y + z = 3x

z = 3x - y ------- eqn 2

The third angle is 15 more than the second

third angle = 15 + second angle

z = 15 + y --------- eqn 3

Substitute eqn 3 in eqn 1

x + y + 15 + y = 180

x + 2y = 165 ---------- eqn 4

Substitute eqn 3 in eqn 2

y + 15 + y = 3x

2y + 15 = 3x

3x - 2y = 15 ---------- eqn 5

Add eqn 4 and eqn 5

x + 2y + 3x - 2y = 165 + 15

4x = 180

x = 45

Substitute x = 45 in eqn 2

y + z = 3(45)

y + z = 135 ----- eqn 6

From eqn 3,

y - z = -15 ----- eqn 7

Add eqn 6 and eqn 7

y + z + y - z = 135 - 15

2y = 120

y = 60

Substitute y = 60 in eqn 3

z = 15 + 60 = 75

z = 75

Thus measure of first angle is 45 degrees and measure of second angle is 60 degrees and measure of third angle is 75 degrees

Answer 2

Answer:

x = 45

y=60

z = 75