Question

select the correct answer. what is the approximate measure of exterior angle b in the polygon? (diagram of quadrilateral with exterior angles: at a: (8x)°, at b: (9x + 3)°, at c: (5x + 4)°, at d: (9x + 5)°; options: a. 87°, b. 96°, c. 104°, d. 116°)

Explanation:

Step1: Recall the sum of exterior angles of a quadrilateral.

The sum of the exterior angles of any polygon is \(360^\circ\). For a quadrilateral, this means the sum of the four exterior angles is \(360^\circ\). So we set up the equation: \(8x + (9x + 3) + (5x + 4) + (9x + 5) = 360\).

Step2: Combine like terms.

Combine the \(x\) terms and the constant terms: \((8x + 9x + 5x + 9x) + (3 + 4 + 5) = 360\). This simplifies to \(31x + 12 = 360\).

Step3: Solve for \(x\).

Subtract 12 from both sides: \(31x = 360 - 12 = 348\). Then divide both sides by 31: \(x=\frac{348}{31}\approx11.23\).

Step4: Find the measure of exterior angle B.

Exterior angle B is \((9x + 3)^\circ\). Substitute \(x\approx11.23\) into the expression: \(9(11.23)+3 = 101.07 + 3 = 104.07^\circ\approx104^\circ\).

Answer:

C. \(104^\circ\)