Question

refer to the figure. if (mangle2=(a + 15)^{circ}) and (mangle3=(a + 35)^{circ}), find the value of a such that (overrightarrow{hl}perpoverrightarrow{hj}).

Explanation:

Step1: Recall perpendicular - angle property

If $HL\perp HJ$, then $\angle JHL = 90^{\circ}$, and $\angle2+\angle3 = 90^{\circ}$.

Step2: Substitute angle measures

Since $m\angle2=(a + 15)^{\circ}$ and $m\angle3=(a + 35)^{\circ}$, we have the equation $(a + 15)+(a + 35)=90$.

Step3: Simplify the left - hand side of the equation

Combine like terms: $a+a+15 + 35=90$, which simplifies to $2a+50 = 90$.

Step4: Solve for a

Subtract 50 from both sides: $2a=90 - 50$, so $2a=40$. Then divide both sides by 2: $a = 20$.

Answer:

$a = 20$