Question
∠1 and ∠2 are complementary angles. If m∠1 = (x + 24)∘ and m∠2 = (5x - 18)∘, then find the measure of ∠1.
Answers
Answered by
GPT 3.5
Complementary angles add up to 90 degrees.
So, we have:
∠1 + ∠2 = 90
Substitute the given expressions for ∠1 and ∠2:
(x + 24) + (5x - 18) = 90
6x + 6 = 90
6x = 84
x = 14
Now, find the measure of ∠1 using the expression for ∠1:
m∠1 = (x + 24) = (14 + 24) = 38 degrees
Therefore, the measure of ∠1 is 38 degrees.
So, we have:
∠1 + ∠2 = 90
Substitute the given expressions for ∠1 and ∠2:
(x + 24) + (5x - 18) = 90
6x + 6 = 90
6x = 84
x = 14
Now, find the measure of ∠1 using the expression for ∠1:
m∠1 = (x + 24) = (14 + 24) = 38 degrees
Therefore, the measure of ∠1 is 38 degrees.