Question

∠1 and ∠2 are complementary angles. m∠1 = 6x + 1 and m∠2 = 6x + 5. draw a diagram, then solve to answer the following questions. x = m∠1 = m∠2 =

Explanation:

Step1: Recall complementary - angle property

Complementary angles sum to 90 degrees. So, $m\angle1 + m\angle2=90$.
Substitute the given expressions: $(6x + 1)+(6x + 5)=90$.

Step2: Simplify the left - hand side

Combine like terms: $6x+6x + 1 + 5=90$, which gives $12x+6 = 90$.

Step3: Solve for x

Subtract 6 from both sides: $12x=90 - 6=84$.
Divide both sides by 12: $x=\frac{84}{12}=7$.

Step4: Find $m\angle1$

Substitute $x = 7$ into the expression for $m\angle1$: $m\angle1=6x + 1=6\times7+1=42 + 1=43$.

Step5: Find $m\angle2$

Substitute $x = 7$ into the expression for $m\angle2$: $m\angle2=6x + 5=6\times7+5=42+5=47$.

Answer:

$x = 7$
$m\angle1 = 43$
$m\angle2 = 47$