Question

solve for y.
(there is a pentagon with angles: 90°, 135°, y°, 88°, 112°)
options: 115, 130, 108, 90

Explanation:

Step1: Recall the formula for the sum of interior angles of a polygon. For an n - sided polygon, the sum of interior angles is \((n - 2)\times180^{\circ}\). This is a pentagon (\(n = 5\)), so the sum of interior angles is \((5 - 2)\times180^{\circ}= 540^{\circ}\).

Step2: Identify the known angles. The known angles are \(90^{\circ}\) (right angle), \(135^{\circ}\), \(112^{\circ}\), \(88^{\circ}\), and the unknown angle \(y^{\circ}\).

Step3: Set up the equation. The sum of all interior angles of the pentagon is equal to the sum of the known angles plus \(y\). So, \(90 + 135+112 + 88+y=540\).

Step4: Calculate the sum of the known angles. \(90+135 = 225\), \(225+112 = 337\), \(337 + 88=425\). So the equation becomes \(425 + y=540\).

Step5: Solve for \(y\). Subtract 425 from both sides of the equation: \(y=540 - 425 = 115\).

Answer:

115