Angles A and B are complementary. Two separate angles are shown. Angle A is (x + 22) degrees. Angle B is x degrees. What is the value of x? 34 56 68 79
The correct answer and explanation is:
Let’s analyze the problem step-by-step.
Problem Recap:
- Angles A and B are complementary.
- Angle A = x+22x + 22 degrees
- Angle B = xx degrees
- Find the value of xx.
Step 1: Understand what “complementary” means
Two angles are complementary if their measures add up to 90 degrees.
Mathematically: A+B=90∘A + B = 90^\circ
Step 2: Set up the equation
Given: A=x+22A = x + 22 B=xB = x
Since they are complementary: (x+22)+x=90(x + 22) + x = 90
Simplify: 2x+22=902x + 22 = 90
Step 3: Solve for xx
Subtract 22 from both sides: 2x=90−222x = 90 – 22 2x=682x = 68
Divide both sides by 2: x=682=34x = \frac{68}{2} = 34
Final answer:
34\boxed{34}
Explanation in detail:
Complementary angles always sum to 90 degrees. In this problem, you have two angles expressed in terms of xx, and since they add to 90 degrees, you can form an equation that represents this relationship.
By substituting the expressions for angles A and B into the equation A+B=90A + B = 90, you get a linear equation in terms of xx. Simplifying this equation gives you 2x+22=902x + 22 = 90.
You then isolate xx by subtracting 22 from both sides and dividing by 2, resulting in x=34x = 34.
This means angle B measures 34 degrees, and angle A measures 34+22=5634 + 22 = 56 degrees. Together, 34+56=9034 + 56 = 90, confirming that they are complementary.
Therefore, the value of xx is 34 degrees.