Question

the angle measurements in the diagram are represented by the following expressions.
∠a = 6x + 5° ∠b = 4x + 45°
solve for x and then find the measure of ∠a:
∠a = □°

Explanation:

Step1: Set up the equation

Since $\angle A$ and $\angle B$ are corresponding angles (assuming the lines are parallel), they are equal. So we set up the equation $6x + 5=4x + 45$.

Step2: Solve for $x$

Subtract $4x$ from both sides: $6x-4x + 5=4x-4x + 45$, which simplifies to $2x+5 = 45$. Then subtract 5 from both sides: $2x+5 - 5=45 - 5$, getting $2x=40$. Divide both sides by 2: $x=\frac{40}{2}=20$.

Step3: Find the measure of $\angle A$

Substitute $x = 20$ into the expression for $\angle A$. $\angle A=6x + 5=6\times20+5=120 + 5=125^{\circ}$.

Answer:

$125$