Question

in the figure, ( mangle1=(7x + 8)^{circ}), ( mangle2=(4x + 12)^{circ}), and ( mangle4=(12x + 11)^{circ}). your friend incorrectly says that ( mangle4 = 61^{circ}). what is ( mangle4)? what mistake might your friend have made? ( mangle4=square^{circ})

Explanation:

Step1: Use the exterior angle theorem

The exterior angle theorem states that \(m\angle4=m\angle1 + m\angle2\). So, \((12x + 11)=(7x + 8)+(4x + 12)\).

Step2: Simplify the equation

Simplify the right - hand side: \((7x + 8)+(4x + 12)=7x+4x + 8 + 12=11x+20\). The equation becomes \(12x + 11=11x + 20\).

Step3: Solve for \(x\)

Subtract \(11x\) from both sides: \(12x-11x+11=11x - 11x+20\), which gives \(x+11 = 20\). Then subtract \(11\) from both sides: \(x=20 - 11=9\).

Step4: Find \(m\angle4\)

Substitute \(x = 9\) into \(m\angle4=(12x + 11)^{\circ}\). So, \(m\angle4=12\times9+11=108 + 11=119^{\circ}\).

Answer:

\(119\)