Find the measure of an angle if its measure is 26 degrees more than 3 times its complement.
16
141
74
42
Trying to figure it out but can't. Please help?
angle: x
complement: 90-x
x = 26+3(90-x)
x = 74
It's 74 guys
Still can't figure it out:(
Well, let's give it a shot! Remember that two angles are considered complementary if their measures add up to 90 degrees. Let's call the measure of our mystery angle "x" and its complement "y." According to the information given, we know that x = 3y + 26. We also know that x + y = 90. Now, let's solve these two equations together.
Substituting the value of x from the first equation into the second equation, we get (3y + 26) + y = 90. Simplifying it, we have 4y + 26 = 90. By subtracting 26 from both sides, we have 4y = 64. Lastly, dividing both sides by 4, we find that y = 16.
So, the complement of our mystery angle is 16 degrees. To find the measure of the angle, we substitute this value back into the first equation: x = 3(16) + 26. Simplifying it, x = 48 + 26 = 74.
Therefore, the measure of the angle is 74 degrees. So, the correct answer is 74.
To find the measure of the angle, let's first understand the concept of a complementary angle. Complementary angles are two angles whose measures add up to 90 degrees.
Let's assume the angle we're trying to find is represented by 'x' degrees. Its complement (the other angle that, when added together with the original angle, equals 90 degrees) will be represented by '(90 - x)' degrees.
According to the problem statement, the measure of the angle is 26 degrees more than 3 times its complement. So, we can write this as an equation:
x = 3(90 - x) + 26
Now, let's solve this equation to find the value of 'x':
x = 3(90 - x) + 26
x = 270 - 3x + 26
4x = 296
x = 74
Therefore, the measure of the angle is 74 degrees. So, the correct answer is 74.