Question

q.13 interior angles of polygons
what is x?
100°
95°
135°
90°
x =

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 pentagon (\(n=5\)), the sum \(S=(5 - 2)\times180^{\circ}=540^{\circ}\).

Step2: Set up an equation using the given angles

We know that \(100^{\circ}+95^{\circ}+135^{\circ}+90^{\circ}+x = 540^{\circ}\).
First, add the known angles: \(100 + 95+135 + 90=(100+95)+(135 + 90)=195+225 = 420^{\circ}\).
Then the equation becomes \(420^{\circ}+x=540^{\circ}\).

Step3: Solve for \(x\)

Subtract \(420^{\circ}\) from both sides of the equation: \(x=540^{\circ}-420^{\circ}\).

Answer:

\(120\)