Question

find the values of x and y. (x + 4)° 76° 124° y°

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. The angle \((x + 4)^{\circ}\) and the angle adjacent to the \(76^{\circ}\) angle are vertical angles. The sum of an angle and its adjacent angle is \(180^{\circ}\). So, \(x + 4+76=180\).

Step2: Solve for \(x\)

First, simplify the left - hand side of the equation \(x + 4+76=180\) to get \(x + 80=180\). Then subtract 80 from both sides: \(x=180 - 80\), so \(x = 100\).

Step3: Use angle - sum property

The sum of the angles around a point is \(360^{\circ}\). We know one angle is \(124^{\circ}\), another is \(76^{\circ}\), and the angle \((x + 4)^{\circ}=104^{\circ}\). Let's find \(y\). So, \(104+76 + 124+y=360\).

Step4: Solve for \(y\)

First, add the known angles: \(104+76+124 = 304\). Then the equation becomes \(304 + y=360\). Subtract 304 from both sides: \(y=360 - 304\), so \(y = 56\).

Answer:

\(x = 100\), \(y = 56\)