Question

use an algebraic equation to find the measure of each angle that is represented in terms of x. the four angle measures are degrees (type a whole number. use a comma to separate answers as needed.)

Explanation:

Step1: Recall the formula for the sum of interior angles of a polygon

The sum of interior angles of an \(n -\)sided polygon is \((n - 2)\times180^{\circ}\). For a heptagon (\(n=7\)), the sum \(S=(7 - 2)\times180^{\circ}=900^{\circ}\).

Step2: Set up the equation

We have the angles \(150^{\circ},140^{\circ},x,x,x + 5^{\circ},x + 5^{\circ}\). So the equation is \(150+140+x+x+x + 5+x + 5=900\).

Step3: Simplify the left - hand side of the equation

Combine like terms: \((150 + 140+5 + 5)+(x+x+x+x)=900\), which simplifies to \(300+4x=900\).

Step4: Solve for \(x\)

Subtract \(300\) from both sides: \(4x=900 - 300\), so \(4x=600\). Then divide both sides by \(4\): \(x=\frac{600}{4}=150\).

Step5: Find the measures of all angles

The angles \(x = 150^{\circ}\), \(x+5=150 + 5=155^{\circ}\).

Answer:

\(150,150,150,155,155\)