Question

∠1 and ∠2 are complementary angles. if m∠1=(x - 1)° and m∠2=(4x - 4)°, then find the measure of ∠1.

Explanation:

Step1: Recall complementary - angle property

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

Step2: Substitute the given angle - measures

Substitute $m\angle1=(x - 1)^{\circ}$ and $m\angle2=(4x - 4)^{\circ}$ into the equation: $(x - 1)+(4x - 4)=90$.

Step3: Simplify the left - hand side of the equation

Combine like terms: $x-1 + 4x-4=5x-5$. So, $5x-5 = 90$.

Step4: Solve for x

Add 5 to both sides of the equation: $5x-5 + 5=90 + 5$, which gives $5x=95$. Then divide both sides by 5: $x=\frac{95}{5}=19$.

Step5: Find the measure of $\angle1$

Substitute $x = 19$ into the expression for $m\angle1$: $m\angle1=(x - 1)^{\circ}=(19 - 1)^{\circ}=18^{\circ}$.

Answer:

$18^{\circ}$