Question

yk\jq 2. y (5x - 15)° (4x + 6)° (3x + 27)° k j

Explanation:

1. Recall the property of a rectangle:

• In a rectangle, all angles are right - angles, and the sum of the interior angles of a quadrilateral is \(360^{\circ}\). Also, opposite angles of a rectangle are equal.
• Let's assume the given figure is a rectangle. We know that the sum of the interior angles of a quadrilateral \(QYKJ\) is \(360^{\circ}\), and since it's a rectangle, we can set up an equation using the angle measures \((4x + 6)^{\circ}\), \((5x-15)^{\circ}\), \((3x + 27)^{\circ}\), and \(90^{\circ}\).
• The sum of the angles is \((4x + 6)+(5x-15)+(3x + 27)+90=360\).

1. Combine like - terms:

• First, combine the \(x\) terms and the constant terms on the left - hand side of the equation.
• \((4x+5x + 3x)+(6-15 + 27)+90=360\).
• \(12x+(6 + 27-15)+90=360\).
• \(12x+(33 - 15)+90=360\).
• \(12x + 18+90=360\).
• \(12x+108 = 360\).

1. Solve for \(x\):

• Subtract 108 from both sides of the equation:
• \(12x+108-108=360 - 108\).
• \(12x=252\).
• Divide both sides by 12:
• \(\frac{12x}{12}=\frac{252}{12}\).
• \(x = 21\).

1. Find the measure of each angle:

• For the angle \((4x + 6)^{\circ}\), substitute \(x = 21\): \(4\times21+6=84 + 6=90^{\circ}\).
• For the angle \((5x-15)^{\circ}\), substitute \(x = 21\): \(5\times21-15=105 - 15=90^{\circ}\).
• For the angle \((3x + 27)^{\circ}\), substitute \(x = 21\): \(3\times21+27=63 + 27=90^{\circ}\).

Step1: Set up angle - sum equation

\((4x + 6)+(5x-15)+(3x + 27)+90=360\)

Step2: Combine like - terms

\(12x+18 + 90=360\)

Step3: Isolate the variable term

\(12x=360 - 108\)

Step4: Solve for \(x\)

\(x=\frac{252}{12}=21\)

Answer:

\(x = 21\)