If The sum of the measures of two complementary angles is 90° and If one angle measures 15° more than twice the measure of its complement, find the measure of each angle. What is The measure of one angle is 1 times the measure of the other. Find the measure of each angle. Show all work.

If one angle = x, the other will be 2x +15

x + (2x+15) = 90

1 times the other means they are equal.

di ko maintindihan iyan buddy

buddy pakilinaw mo nga
ang nakuha ko kasi buddy ay
25 and 65 degrees buddy
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salamat buddy

Let's assume one angle is represented by x, and the other angle is represented by y (complement of x).

According to the given information:
1) The sum of the measures of two complementary angles is 90°, so we can write the equation: x + y = 90

2) One angle measures 15° more than twice the measure of its complement, so we can write the equation: x = 2y + 15

Now we have a system of two equations with two variables. We can solve this system to find the values of x and y.

From equation 1, we can rewrite it as y = 90 - x.

Substitute this value of y into equation 2:
x = 2(90 - x) + 15

Expand the equation:
x = 180 - 2x + 15
x = 195 - 2x

Move the variables to one side:
3x = 195

Divide both sides by 3:
x = 65

Substitute the value of x into equation 1 to find y:
65 + y = 90
y = 90 - 65
y = 25

Therefore, the measure of one angle is 65° and the measure of the other angle is 25°.

To solve this problem, let's assign variables to the unknown angles. Let's call one angle 'x' and the other angle 'y'.

According to the problem, the sum of two complementary angles is 90°, so we have the equation:

x + y = 90 --(Equation 1)

The problem also states that one angle measures 15° more than twice the measure of its complement. In equation form, we have:

x = 2y + 15 --(Equation 2)

Additionally, the problem mentions that one angle measures 1 times the measure of the other angle. In equation form, we have:

x = y --(Equation 3)

Now, we have a system of three equations (Equations 1, 2, and 3) that we can solve simultaneously to find the values of x and y.

To solve the system, we can use the substitution method or the elimination method. Let's use the substitution method:

From Equation 3, we can substitute 'x' in the other equations:

In Equation 1: y + y = 90
2y = 90
Divide both sides of the equation by 2:
y = 45

Now, substitute the value of y back into Equation 3 to find x:

x = 45

Therefore, the measure of each angle is x = 45° and y = 45°.