Question

angles of a triangle

The second angle of a garden triangle is four times as large as the first. the third angle is 45 degrees less than the sum of the other two angles. find the measure of each angle.

15 x 4=60 x 3 = 180
side a=15
side b = 60
sIDE C = 3

Answer 1

(angle 1) + (angle 2) + (angle 3) = 180

Let's make an angle Q = (angle 1) + (angle 2).

SO...

Q + (angle 3) = 180
AND
(angle 3) = Q - 45.

SO...
Q + (Q - 45) = 180
2Q = 225
Q = 112.5

Going back to the equation Q + (angle 3) = 180 or by rearranging it: (angle 3) = 180 - Q,
if Q = 112.5, then (angle 3) = 180 - 112.5 = 67.5

ANGLE 3 = 67.5

if angle two is four times the size of angle one, then
(angle 1) + 4(angle 1) = Q, where Q = 112.5
SO...
5(angle 1) = 112.5

ANGLE 1 = 22.5

(angle 1) + (angle 2) + (angle 3) = 180
22.5 + (angle 2) + 67.5 = 180

ANGLE 2 = 90