Question

angles a and b are complementary. what is the value of x? (x+22)° at angle a, x° at angle b. options: 34, 56, 68, 79.

Explanation:

Step1: Recall complementary angles property

Complementary angles sum to \(90^\circ\). So, \((x + 22) + x = 90\).

Step2: Simplify the equation

Combine like terms: \(2x + 22 = 90\).

Step3: Solve for x

Subtract 22 from both sides: \(2x = 90 - 22 = 68\). Then divide by 2: \(x = \frac{68}{2} = 34\). Wait, no, wait—wait, no, let's check again. Wait, \((x + 22) + x = 90\) → \(2x + 22 = 90\) → \(2x = 90 - 22 = 68\) → \(x = 34\)? But wait, the options have 34, 56, etc. Wait, maybe I made a mistake. Wait, no—wait, angle A is \((x + 22)^\circ\), angle B is \(x^\circ\), and they are complementary, so sum to 90. So:

\((x + 22) + x = 90\)

\(2x + 22 = 90\)

\(2x = 90 - 22 = 68\)

\(x = 34\). Wait, but let's check the options. 34 is an option. Wait, but maybe I misread the angles. Wait, maybe angle A is \((x + 22)\) and angle B is \(x\), and they are complementary. So the calculation is correct. So x is 34? Wait, but let's check again. Wait, 34 + 22 = 56, and 34 + 56 = 90. Yes, that works. So x is 34.

Wait, but the options are 34, 56, 68, 79. So 34 is correct.

Answer:

34