Question

g r (3x + 13)° (5x - 25)° (x + 66)° (4x - 6)° m w grwm __________

Explanation:

Step1: Recall the property of a quadrilateral

The sum of the interior - angles of a quadrilateral is 360°. So, we set up the equation: \((3x + 13)+(5x-25)+(x + 66)+(4x-6)=360\).

Step2: Combine like - terms

Combine the \(x\) terms and the constant terms: \((3x+5x+x + 4x)+(13-25 + 66-6)=360\), which simplifies to \(13x + 48=360\).

Step3: Solve for \(x\)

Subtract 48 from both sides of the equation: \(13x=360 - 48\), so \(13x=312\). Then divide both sides by 13: \(x=\frac{312}{13}=24\).

Step4: Find the measure of each angle

• Angle \(G=(3x + 13)^{\circ}=(3\times24 + 13)^{\circ}=(72 + 13)^{\circ}=85^{\circ}\).
• Angle \(R=(5x-25)^{\circ}=(5\times24-25)^{\circ}=(120 - 25)^{\circ}=95^{\circ}\).
• Angle \(W=(4x-6)^{\circ}=(4\times24-6)^{\circ}=(96 - 6)^{\circ}=90^{\circ}\).
• Angle \(M=(x + 66)^{\circ}=(24+66)^{\circ}=90^{\circ}\).

Since two pairs of adjacent angles are supplementary (\(85^{\circ}+95^{\circ}=180^{\circ}\) and \(90^{\circ}+90^{\circ}=180^{\circ}\)), and there are two right - angles, the quadrilateral \(GRWM\) is a rectangle.

Answer:

Rectangle