Question
Determine the measure of the complementary angles in the figure shown. Remember that complementary angles add up to 90 degrees. Step 1: set up an equation and solve for x step 2: find the value of the angles. Marked angles : x and 2x
Answers
GPT-4o mini
To find the measures of the complementary angles marked \(x\) and \(2x\), we first set up an equation based on the definition of complementary angles. Since complementary angles add up to \(90^\circ\), we can write the equation:
\[
x + 2x = 90
\]
Now we can simplify the left side:
\[
3x = 90
\]
Next, we solve for \(x\) by dividing both sides by 3:
\[
x = \frac{90}{3} = 30
\]
Now that we have \(x\), we can find \(2x\):
\[
2x = 2 \times 30 = 60
\]
Thus, the measures of the angles are:
- \(x = 30^\circ\)
- \(2x = 60^\circ\)
So, the two complementary angles measure \(30^\circ\) and \(60^\circ\).
\[
x + 2x = 90
\]
Now we can simplify the left side:
\[
3x = 90
\]
Next, we solve for \(x\) by dividing both sides by 3:
\[
x = \frac{90}{3} = 30
\]
Now that we have \(x\), we can find \(2x\):
\[
2x = 2 \times 30 = 60
\]
Thus, the measures of the angles are:
- \(x = 30^\circ\)
- \(2x = 60^\circ\)
So, the two complementary angles measure \(30^\circ\) and \(60^\circ\).