Question

example: if m∠3=(4x + 7)° and m∠6=(5x - 13)°, find the value of x.
check: find the value of y if m∠8 = 68° and m∠3=(3y - 2)°.
check for understanding: two parallel lines, f and g, are cut by a transversal, h, as shown.
what are the values of x and y?
x=

y=

Explanation:

Step1: Identify angle - relationship for \(y\)

\(\angle 8\) and \(\angle 3\) are vertical angles. Vertical angles are equal. So we set up the equation \(3y - 2=68\).

Step2: Solve the equation for \(y\)

Add 2 to both sides of the equation: \(3y-2 + 2=68 + 2\), which simplifies to \(3y=70\). Then divide both sides by 3: \(y=\frac{70}{3}\).

Step3: Identify angle - relationship for \(x\)

The angle of \(64^{\circ}\) and \((x + y)^{\circ}\) are corresponding angles. Since the lines are parallel, corresponding angles are equal. So \(x + y=64\).

Step4: Substitute \(y=\frac{70}{3}\) into \(x + y=64\)

We get \(x+\frac{70}{3}=64\). Subtract \(\frac{70}{3}\) from both sides: \(x = 64-\frac{70}{3}=\frac{192 - 70}{3}=\frac{122}{3}\).

Answer:

\(x=\frac{122}{3}\), \(y=\frac{70}{3}\)