Question

homework - complementary ang
due sep 5 by 11:58pm points 10 submitting an
given:
∠a = 6x + 25
∠b = 4x - 1

Explanation:

Step1: Identify angle relationship

Since the angles form a right angle (as indicated by the square corner), they are complementary. So, $\angle A + \angle B = 90^\circ$.
Substitute the given expressions: $(6x + 25) + (4x - 1) = 90$.

Step2: Simplify the equation

Combine like terms: $6x + 4x + 25 - 1 = 90$ → $10x + 24 = 90$.

Step3: Solve for x

Subtract 24 from both sides: $10x = 90 - 24$ → $10x = 66$.
Divide by 10: $x = \frac{66}{10} = 6.6$. (If we need to find angle measures, substitute back: $\angle A = 6(6.6)+25 = 39.6 + 25 = 64.6^\circ$, $\angle B = 4(6.6)-1 = 26.4 - 1 = 25.4^\circ$; sum is $64.6 + 25.4 = 90^\circ$, which checks out.)

Answer:

If solving for \( x \), \( x = 6.6 \) (or \( \frac{33}{5} \)). If finding angles, \( \angle A = 64.6^\circ \), \( \angle B = 25.4^\circ \) (depending on the question's requirement).