Question

∠5 and ∠6 are complementary angles. m∠5 = 3x + 6 and m∠6 = 4x. draw a diagram, then solve to answer the following questions. x = m∠5 = m∠6 =

Explanation:

Step1: Recall complementary - angle property

Complementary angles sum to 90 degrees. So, $m\angle5 + m\angle6=90$.

Step2: Substitute angle expressions

Substitute $m\angle5 = 3x + 6$ and $m\angle6 = 4x$ into the equation: $(3x + 6)+4x=90$.

Step3: Combine like - terms

$3x+4x + 6=90$, which simplifies to $7x+6 = 90$.

Step4: Solve for x

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

Step5: Find $m\angle5$

Substitute $x = 12$ into the expression for $m\angle5$: $m\angle5=3x + 6=3\times12+6=36 + 6=42$.

Step6: Find $m\angle6$

Substitute $x = 12$ into the expression for $m\angle6$: $m\angle6=4x=4\times12 = 48$.

Answer:

$x = 12$
$m\angle5 = 42$
$m\angle6 = 48$