Question

11 find the value of $x$ in the regular pentagon. $(2x + 13)^{circ}$ $x = \boldsymbol{\square}$

Explanation:

Step1: Find interior angle sum

The formula for the sum of interior angles of an n-sided polygon is $(n-2)\times180^\circ$. For a pentagon, $n=5$.
$\text{Sum}=(5-2)\times180^\circ = 540^\circ$

Step2: Find one interior angle

In a regular pentagon, all interior angles are equal. Divide the total sum by 5.
$\text{One interior angle}=\frac{540^\circ}{5}=108^\circ$

Step3: Set up equation and solve

Set the given angle equal to 108° and solve for $x$.
$2x + 13 = 108$
$2x = 108 - 13$
$2x = 95$
$x=\frac{95}{2}=47.5$

Answer:

$47.5$