Final answer:
By setting up an equation based on the given relationship between angle A and angle B, we find that angle A is 50 degrees and angle B is 40 degrees. Therefore correct option is C
Step-by-step explanation:
The sum of angle A and angle B is given as 90 degrees. Furthermore, angle A is described as being 30 degrees less than twice the measure of angle B. To find the measures of the angles, we can set up a system of equations based on the provided information:
Let angle B be represented by 'b'. Then, since angle A is 30 degrees less than twice angle B, angle A can be represented as '2b - 30'.
The sum of the angles is 90 degrees, leading to the equation:
A + B = 90
Which can be rewritten as:
2b - 30 + b = 90
Combining like terms, we get:
3b - 30 = 90
Adding 30 to both sides of the equation, we obtain:
3b = 120
Dividing both sides by 3, we determine:
b = 40
Now that we know angle B is 40 degrees, we can find angle A by plugging angle B's measure into the expression for angle A:
A = 2b - 30
So:
A = 2(40) - 30A
= 80 - 30A
= 50
Therefore, angle A is 50 degrees and angle B is 40 degrees. This matches one of the multiple-choice options provided.