Question

in the figure below, m∠1=(x + 14)° and m∠2=3x°. find the angle measures.

Explanation:

Step1: Set up equation based on angle - sum

Since $\angle1$ and $\angle2$ are complementary (the angle formed by the two is a right - angle, $90^{\circ}$), we have the equation $(x + 14)+3x=90$.
$(x + 14)+3x=90$ simplifies to $x+14 + 3x=90$, then $4x+14 = 90$.

Step2: Solve for $x$

Subtract 14 from both sides of the equation $4x+14 = 90$.
$4x=90 - 14$, so $4x=76$.
Divide both sides by 4: $x=\frac{76}{4}=19$.

Step3: Find measure of $\angle1$

Substitute $x = 19$ into the expression for $m\angle1$.
$m\angle1=(x + 14)^{\circ}=(19 + 14)^{\circ}=33^{\circ}$.

Step4: Find measure of $\angle2$

Substitute $x = 19$ into the expression for $m\angle2$.
$m\angle2=3x^{\circ}=3\times19^{\circ}=57^{\circ}$.

Answer:

$m\angle1 = 33^{\circ}$
$m\angle2 = 57^{\circ}$