Question

find the measure of $\angle g$.

angle	measure
$\angle b$	$128^\circ$
$\angle c$	$127^\circ$
$\angle d$	$135^\circ$
$\angle e$	$122^\circ$
$\angle f$	$126^\circ$

Explanation:

Step1: Recall the formula for the sum of interior angles of a polygon.

The formula for the sum of interior angles of a polygon with \( n \) sides is \( (n - 2)\times180^\circ \). A heptagon (7 - sided polygon) has \( n = 7 \), so the sum is \( (7 - 2)\times180^\circ = 5\times180^\circ = 900^\circ \).

Step2: Calculate the sum of the given angles.

Sum of given angles: \( 130^\circ + 128^\circ + 127^\circ + 135^\circ + 122^\circ + 126^\circ \)
\[

$$\begin{align*} &130 + 128 = 258\\ &258 + 127 = 385\\ &385 + 135 = 520\\ &520 + 122 = 642\\ &642 + 126 = 768 \end{align*}$$

\]

Step3: Find the measure of \( \angle G \).

Let \( m\angle G = x \). Then \( 768^\circ + x = 900^\circ \). Solving for \( x \), we get \( x = 900^\circ - 768^\circ = 132^\circ \).

Answer:

\( 132^\circ \)