Question

find the value of a. then find the angle measures of the quadrilateral. sum of angle measures: 360°. the angle measures from least to greatest are

Explanation:

Step1: Set up equation

The sum of the interior - angles of a quadrilateral is 360°. So, \(a + 2a+2a + a=360\).
Combining like - terms, we get \(6a = 360\).

Step2: Solve for a

Divide both sides of the equation \(6a = 360\) by 6. So, \(a=\frac{360}{6}=60\).

Step3: Find angle measures

The angle measures are:

• First angle: \(a = 60^{\circ}\)
• Second angle: \(2a=2\times60 = 120^{\circ}\)
• Third angle: \(2a = 120^{\circ}\)
• Fourth angle: \(a = 60^{\circ}\)

Answer:

\(a = 60\); The angle measures from least to greatest are \(60^{\circ},60^{\circ},120^{\circ},120^{\circ}\)