Question

in the figure below, (mangle1=(x + 33)^{circ}) and (mangle2 = 2x^{circ}). find the angle - measures.

Explanation:

Step1: Set up equation

Since $\angle1$ and $\angle2$ are complementary (as they form a right - angle), we have $(x + 33)+2x=90$.

Step2: Combine like terms

$x+2x+33 = 90$, which simplifies to $3x+33 = 90$.

Step3: Isolate the variable term

Subtract 33 from both sides: $3x=90 - 33$, so $3x=57$.

Step4: Solve for x

Divide both sides by 3: $x=\frac{57}{3}=19$.

Step5: Find measure of $\angle1$

Substitute $x = 19$ into the expression for $\angle1$: $m\angle1=(x + 33)=(19+33)=52^{\circ}$.

Step6: Find measure of $\angle2$

Substitute $x = 19$ into the expression for $\angle2$: $m\angle2=2x=2\times19 = 38^{\circ}$.

Answer:

$m\angle1 = 52^{\circ}$
$m\angle2 = 38^{\circ}$