Question

1. ∠1 and ∠2 are complementary angles. find the measures of the angles when m∠1=(3x + 6)° and m∠2=(4x - 14)°. m∠1 = m∠2 =

Explanation:

Step1: Use complementary - angle property

Since $\angle1$ and $\angle2$ are complementary, $m\angle1 + m\angle2=90^{\circ}$. So, $(3x + 6)+(4x - 14)=90$.

Step2: Simplify the left - hand side

Combine like terms: $3x+4x+6 - 14=90$, which gives $7x-8 = 90$.

Step3: Solve for $x$

Add 8 to both sides: $7x=90 + 8=98$. Then divide both sides by 7, so $x=\frac{98}{7}=14$.

Step4: Find $m\angle1$

Substitute $x = 14$ into the expression for $m\angle1$: $m\angle1=3x + 6=3\times14+6=42 + 6=48^{\circ}$.

Step5: Find $m\angle2$

Substitute $x = 14$ into the expression for $m\angle2$: $m\angle2=4x - 14=4\times14-14=56 - 14=42^{\circ}$.

Answer:

$m\angle1 = 48^{\circ}$
$m\angle2 = 42^{\circ}$