Question

the figure is not drawn to scale. 12 if m∠2 = x + 8 and m∠3 = 2x + 7, what is m∠2? 57 33 25 30

Explanation:

Step1: Use angle - sum property of a right - triangle

In a right - triangle, the sum of the two non - right angles is 90 degrees. So, $\angle2+\angle3 = 90^{\circ}$.

Step2: Substitute the given angle expressions

Substitute $m\angle2=x + 8$ and $m\angle3=2x + 7$ into the equation $\angle2+\angle3 = 90^{\circ}$. We get $(x + 8)+(2x+7)=90$.

Step3: Simplify the left - hand side of the equation

Combine like terms: $x+2x+8 + 7=90$, which simplifies to $3x+15 = 90$.

Step4: Solve for x

Subtract 15 from both sides: $3x=90 - 15=75$. Then divide both sides by 3: $x=\frac{75}{3}=25$.

Step5: Find the measure of $\angle2$

Substitute $x = 25$ into the expression for $m\angle2$. So, $m\angle2=x + 8=25+8=33$.

Answer:

33