Question

applying the angle addition postulate
if ( mangle bgf = 152^circ ), what is ( mangle agf )?
options: 64, 92, 180, 240

Explanation:

Step1: Identify the Angle Addition Postulate

The Angle Addition Postulate states that if a point lies in the interior of an angle, the sum of the two smaller angles formed is equal to the measure of the larger angle. Here, $\angle BGF$ is composed of $\angle AGB$ and $\angle AGF$. So, $m\angle BGF = m\angle AGB + m\angle AGF$.
We know $m\angle AGB = 88^\circ$ (from the diagram) and $m\angle BGF = 152^\circ$.

Step2: Solve for $m\angle AGF$

Rearrange the formula: $m\angle AGF = m\angle BGF - m\angle AGB$.
Substitute the known values: $m\angle AGF = 152^\circ - 88^\circ$.
Calculate the result: $152 - 88 = 64$. So, $m\angle AGF = 64^\circ$.

Answer:

$64^\circ$