Two antles are complimentary. The sum of the measure of the first angle and half the second angle is 83. Find measure of angles.
What is the measure of the smaller angle?
What is the measure of the other angles?
It would help if you proofread your questions before you posted them. "Other angles"?
Let A = first angle and B = second angle.
A + B = 90º
A + B/2 = 83º
Subtract second equation from the first.
B/2 = 7º
B = 14º
Insert that value into the first equation and solve for A. Check by inserting both values into the second equation.
Let's assume the measure of the first angle is denoted by "x", and the measure of the second angle is denoted by "y".
Given that the angles are complementary, we know that x + y = 90 degrees.
We are also given that the sum of the measure of the first angle and half the second angle is 83 degrees, which can be written as:
x + (1/2)*y = 83
We can now solve these two equations to find the values of x and y.
Let's multiply the second equation by 2 to eliminate the fraction:
2*(x + (1/2)*y) = 2*83
2x + y = 166
Now we have a system of equations:
x + y = 90
2x + y = 166
To solve this system, we can subtract the first equation from the second equation:
(2x + y) - (x + y) = 166 - 90
x = 76
Substituting the value of x back into the first equation:
76 + y = 90
y = 90 - 76
y = 14
Therefore, the measure of the smaller angle is 14 degrees, and the measure of the other angle is 76 degrees.
To find the measure of the smaller angle, let's assume it as "x".
We know that the two angles are complementary, which means their sum is 90 degrees.
If the smaller angle is "x", then the larger angle would be 90 - x, as they are complementary.
The problem also states that the sum of the measure of the first angle and half the measure of the second angle is 83.
So, we can write the equation as:
x + (1/2)*(90 - x) = 83
Now, we can solve this equation to find the value of x.
Let's simplify the equation:
2x + (90 - x)/2 = 83
2x + (90 - x)/2 = 83
4x + 90 - x = 166
3x = 76
x = 76/3
x ≈ 25.33
Therefore, the measure of the smaller angle is approximately 25.33 degrees.
To find the measure of the larger angle, we can substitute the value of x into the equation:
90 - x ≈ 90 - 25.33
≈ 64.67
Therefore, the measure of the larger angle is approximately 64.67 degrees.