Question

in the figure, m∠1=(x + 14)° and m∠2=(3x)°. (a) write an equation to find x. make sure you use an \=\ sign in your answer. equation: (b) find the degree measure of each angle. m∠1= ° m∠2= °

Explanation:

Step1: Set up the equation

Since the two angles are complementary (assuming they form a right - angle as they seem to be adjacent and form a 90 - degree angle), we have $(x + 14)+3x=90$.

Step2: Combine like terms

Combining the $x$ terms on the left - hand side gives $4x+14 = 90$.

Step3: Isolate the variable term

Subtract 14 from both sides: $4x=90 - 14$, so $4x=76$.

Step4: Solve for x

Divide both sides by 4: $x=\frac{76}{4}=19$.

Step5: Find the measure of angle 1

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

Step6: Find the measure of angle 2

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

Answer:

(a) Equation: $(x + 14)+3x=90$
(b) $m\angle1 = 33^{\circ}$
$m\angle2 = 57^{\circ}$