Q. The sum of the measures of two supplementary angels is 180 degrees. If one angel measures 45 degrees less than twice the measures of its supplement, find the measure of each angle?
what steps do I need to take in order to get the measurments?
A1 + A2 = 180
2*A1 - 45=A2
I got 45 degrees for the first angle and 135 degrees for the second angle, is that right??
the sum of measures of the angles of any tringle eqals 180 if the degrss measures of the three angles of a triangle are consecutive integers how many degrees are each angle
To find the measure of each angle, we can set up a system of equations using the given information. Let's say the measure of one angle is A1 and the measure of its supplement is A2.
Step 1: Set up the first equation using the fact that the sum of the measures of two supplementary angles is 180 degrees:
A1 + A2 = 180
Step 2: Set up the second equation using the fact that one angle measures 45 degrees less than twice the measure of its supplement:
2*A2 - 45 = A1
Now we have the system of equations:
A1 + A2 = 180
2*A2 - 45 = A1
To solve this system of equations, we can use the method of substitution or elimination. Let's use substitution in this case:
Step 3: Solve the second equation for A1 in terms of A2:
A1 = 2*A2 - 45
Step 4: Substitute the expression for A1 in the first equation:
2*A2 - 45 + A2 = 180
Step 5: Simplify and solve for A2:
3*A2 - 45 = 180
3*A2 = 180 + 45
3*A2 = 225
A2 = 225/3
A2 = 75
Step 6: Substitute the value of A2 back into the equation for A1:
A1 = 2*A2 - 45
A1 = 2*75 - 45
A1 = 150 - 45
A1 = 105
So the measure of the first angle (A1) is 105 degrees, and the measure of the second angle (A2) is 75 degrees.
Your calculations of 45 degrees for the first angle and 135 degrees for the second angle are incorrect. The correct answer is 105 degrees for the first angle and 75 degrees for the second angle.