Question

applying the angle addition postulate
if ( mangle bgf = 152^{circ}), what is ( mangle agf)?

Explanation:

Step1: Identify the angle relationship

We know that \( m\angle BGF = m\angle AGB + m\angle AGF \) by the Angle Addition Postulate. We are given \( m\angle BGF = 152^\circ \) and \( m\angle AGB = 88^\circ \).

Step2: Solve for \( m\angle AGF \)

Substitute the known values into the equation: \( 152^\circ = 88^\circ + m\angle AGF \). Then, subtract \( 88^\circ \) from both sides: \( m\angle AGF = 152^\circ - 88^\circ \).

Step3: Calculate the result

\( 152 - 88 = 64 \), so \( m\angle AGF = 64^\circ \).

Answer:

\( 64 \)