Question

The second angle of a triangle measures seven more than twice that of the first angle and the third angle measures of five more than three times that of the first find the measure of each angle

Answer 1

x = measure of the first angle

y = measure of the second angle

z = measure of the third angle

The second angle of a triangle measures seven more than twice that of the first angle means:

y = 2 x + 7°

The third angle measures of five more than three times that of the first means:

z = 3 x + 5°

The sum of the angles in a triangle is 180°.

x + y + z = 180°

x + 2 x + 7° + 3 x + 5° = 180°

6 x + 12° = 180°

Subtract 12° to both sides.

6 x = 168°

x = 168° / 6 = 28°

y = 2 x + 7° = 2 • 28° + 7° = 56° + 7°

y = 63°

z = 3 x + 5° = 3 • 28° + 5° = 84° + 5°

z = 89°

measure of the first angle = 28°

measure of the second angle = 63°

measure of the third angle = 89°