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

(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

To find the measure of each angle in the triangle, we can use the given information.

Let's represent the first angle as x degrees.

The second angle is four times as large as the first angle, so it would be 4x degrees.

The third angle is 45 degrees less than the sum of the other two angles, which is (x + 4x) - 45 degrees.

Now, we can set up an equation based on the fact that the sum of the angles in a triangle is always 180 degrees.

x + 4x + (x + 4x - 45) = 180

Combine like terms:

10x - 45 = 180

Now, isolate x by adding 45 to both sides:

10x = 225

Divide both sides by 10 to solve for x:

x = 22.5

Now, we can substitute this value back into the equation to find the other two angles:

First angle: x = 22.5 degrees
Second angle: 4x = 4 * 22.5 = 90 degrees
Third angle: (x + 4x - 45) = 5x - 45 = 5 * 22.5 - 45 = 112.5 - 45 = 67.5 degrees

So, the measure of each angle in the triangle is:

First angle: 22.5 degrees
Second angle: 90 degrees
Third angle: 67.5 degrees