Question

if ( x^circ ) and ( (17x + 18)^circ ) are the measures of complementary angles, what is the measure of each angle? the measure of ( x^circ ) is ( square^circ ) the measure of ( (17x + 18)^circ ) is ( square^circ )

Explanation:

Step1: Recall complementary angles sum to 90°

Complementary angles add up to \(90^\circ\). So, we set up the equation: \(x + (17x + 18) = 90\).

Step2: Simplify and solve for \(x\)

Combine like terms: \(18x + 18 = 90\).
Subtract 18 from both sides: \(18x = 90 - 18 = 72\).
Divide both sides by 18: \(x = \frac{72}{18} = 4\).

Step3: Find the measure of each angle

For \(x^\circ\): Substitute \(x = 4\), so it's \(4^\circ\).
For \((17x + 18)^\circ\): Substitute \(x = 4\): \(17(4) + 18 = 68 + 18 = 86^\circ\).

Answer:

The measure of \(x^\circ\) is \(4^\circ\). The measure of \((17x + 18)^\circ\) is \(86^\circ\).