Question

in the figure, ( mangle1=(5x + 11)^{circ}, mangle2=(2x + 16)^{circ} ), and ( mangle3=(8x + 10)^{circ} ). what is ( mangle3 )?

Explanation:

Step1: Use the exterior angle theorem

The exterior angle theorem states that \(m\angle3=m\angle1 + m\angle2\). So, \((8x + 10)=(5x+11)+(2x + 16)\).

Step2: Simplify the equation

Simplify the right - hand side: \((5x+11)+(2x + 16)=5x+2x+11 + 16=7x+27\). The equation becomes \(8x + 10=7x+27\).

Step3: Solve for \(x\)

Subtract \(7x\) from both sides: \(8x-7x+10=7x - 7x+27\), which gives \(x+10=27\). Then subtract \(10\) from both sides: \(x=27 - 10=17\).

Step4: Find \(m\angle3\)

Substitute \(x = 17\) into \(m\angle3=(8x + 10)^{\circ}\). So, \(m\angle3=(8\times17+10)^{\circ}=(136 + 10)^{\circ}=146^{\circ}\).

Answer:

\(146\)