Question

∠1 and ∠2 are complementary angles. if (mangle1=(5x + 19)^{circ}) and (mangle2=(5x + 21)^{circ}), then find the measure of ∠1.

Explanation:

Step1: Recall the definition of complementary angles

Complementary angles add up to 90 degrees. So, $m\angle1 + m\angle2=90^{\circ}$.

Step2: Substitute the given angle - measures

Substitute $m\angle1=(5x + 19)^{\circ}$ and $m\angle2=(5x + 21)^{\circ}$ into the equation: $(5x + 19)+(5x + 21)=90$.

Step3: Simplify the left - hand side of the equation

Combine like terms: $5x+5x+19 + 21=90$, which simplifies to $10x+40 = 90$.

Step4: Solve for x

Subtract 40 from both sides: $10x=90 - 40$, so $10x=50$. Then divide both sides by 10: $x = 5$.

Step5: Find the measure of $\angle1$

Substitute $x = 5$ into the expression for $m\angle1$: $m\angle1=(5x + 19)^{\circ}=(5\times5+19)^{\circ}=(25 + 19)^{\circ}=44^{\circ}$.

Answer:

$44^{\circ}$