Question

angle addition postulate
find x
m∠mfg=(10x + 5)°
(7x + 11)°
30°

Explanation:

Step1: Apply angle - addition postulate

The angle - addition postulate states that \(m\angle MFG=m\angle MFK + m\angle KFG\). So, \((10x + 5)=(7x + 11)+30\).

Step2: Simplify the right - hand side

\((10x + 5)=7x+41\).

Step3: Isolate the variable terms

Subtract \(7x\) from both sides: \(10x-7x + 5=7x-7x + 41\), which gives \(3x+5 = 41\).

Step4: Isolate the variable

Subtract 5 from both sides: \(3x+5 - 5=41 - 5\), so \(3x=36\).

Step5: Solve for \(x\)

Divide both sides by 3: \(x=\frac{36}{3}=12\).

Answer:

\(x = 12\)