Question

in the figure, $overrightarrow{ca}$ and $overrightarrow{ce}$ are opposite rays, $overrightarrow{ch}$ bisects $angle gcd$, and $overrightarrow{gc}$ bisects $angle bgd$. if $mangle bgc=(7x - 2)^{circ}$ and $mangle cgf=(8x - 8)^{circ}$, what is $mangle bgf$? $mangle bgf=(7x - 2)+(8x - 8)$

Explanation:

Step1: Identify angle - addition property

By the angle - addition postulate, \(m\angle BGF=m\angle BGC + m\angle CGF\).

Step2: Substitute the given angle expressions

We are given \(m\angle BGC=(7x - 2)^{\circ}\) and \(m\angle CGF=(8x - 8)^{\circ}\). So \(m\angle BGF=(7x - 2)+(8x - 8)\).

Step3: Simplify the expression

Combine like - terms: \((7x+8x)+(-2 - 8)=15x-10\).

Answer:

\((15x - 10)^{\circ}\)