If 2 angles are complementary and one angle is 6* more than 3 times the other . Find the angl
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Answer:
Two Angles are complementary. One angle is six more than twice the other. What is the measure of each angle?
So the answer depends if you are using degrees or radians.
When using degrees complementary angles sum to 90°.
Let your first angle be x°, then the second angle will be (2x + 6)°.
x° + (2x + 6)° = 90° : simplify by adding like terms
3x° + 6° = 90° : isolate 3x by subtracting 6° from both sides
3x° = 84° ; isolate x by dividing both sides by 3
x° = 28°
The other angle is 2(28°) = 6° = 56° + 6° = 62°
Check: 28° + 62° = 90°
In degrees the two angles are 28°and 62°.
However there is another way to measure angles, it is radians. By mathematical convention, if there is no degree symbol given you are supposed to assume an angle measurement is in degrees. This is why it is important to include a degree symbol if you mean degrees.
In degrees the angle measure of a full circle is 360°, but in radians the angle measure of a full circle is 2π radians. Because 90° is 1/4 of 360°, this means that complementary angles sum to 1/4 of 2π, which is π/2 when measuring in radians.
Let your first angle be x, then the second angle will be 2x + 6.
x + 2x + 6 = π/2 : simplify by adding like terms
3x + 6 = π/2 : isolate 3x by subtracting 6 from both sides
3x = (π/2) - 6; isolate x by dividing both sides by 3
x = (π/6) - 2
The second angle is 2[(π/6) - 2] + 6 = (π/3) - 4 + 6 = (π/3) + 2
Check: (π/6) - 2 + (π/3) + 2 = (π/6) + (π/3) = π/2
In radians the answers are (π/6) - 2 and (π/3) + 2.
Step-by-step explanation: