Question

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

Explanation:

Step1: Use complementary - angle property

Since $\angle5$ and $\angle6$ are complementary, $m\angle5 + m\angle6=90^{\circ}$. So, $(4x + 3)+(3x + 3)=90$.

Step2: Simplify the left - hand side

Combine like terms: $4x+3x + 3 + 3=90$, which gives $7x+6 = 90$.

Step3: Solve for $x$

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

Step4: Find $m\angle5$

Substitute $x = 12$ into the expression for $m\angle5$: $m\angle5=4x + 3=4\times12+3=48 + 3=51^{\circ}$.

Step5: Find $m\angle6$

Substitute $x = 12$ into the expression for $m\angle6$: $m\angle6=3x + 3=3\times12+3=36 + 3=39^{\circ}$.

Answer:

$x = 12$
$m\angle5 = 51^{\circ}$
$m\angle6 = 39^{\circ}$