Question

solve for x. the figure is a pentagon with vertices a, b, c, d, e. angle at a: x + 40°, angle at b: 80°, angle at c: x + 50°, angle at d: x + 5°, angle at e: 125°.

Explanation:

Step1: Use the formula for the sum of interior angles of a pentagon

The sum of interior angles of a pentagon is \((5 - 2)\times180^{\circ}=540^{\circ}\).

Step2: Set up the equation

\((x + 40)+80+(x + 50)+(x + 5)+125 = 540\).

Step3: Simplify the left - hand side of the equation

Combine like terms: \((x+x+x)+(40 + 80+50+5+125)=3x+300\).
So the equation becomes \(3x+300 = 540\).

Step4: Solve for \(x\)

Subtract \(300\) from both sides: \(3x=540 - 300\), \(3x = 240\).
Divide both sides by \(3\): \(x=\frac{240}{3}\).

Answer:

\(x = 80\)