Question

11.
(14x - 13)°
(4x + 13)° (6x + 2)°

Explanation:

Step1: Use exterior angle theorem

The exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. So, we have the equation: \(14x - 13=(4x + 13)+(6x+2)\)

Step2: Simplify the right - hand side

Simplify \((4x + 13)+(6x + 2)\) by combining like terms. \(4x+6x + 13+2=10x+15\). So the equation becomes \(14x-13 = 10x + 15\)

Step3: Solve for x

Subtract \(10x\) from both sides: \(14x-10x-13=10x - 10x+15\), which gives \(4x-13 = 15\). Then add 13 to both sides: \(4x-13 + 13=15 + 13\), so \(4x=28\). Divide both sides by 4: \(x=\frac{28}{4}=7\)

Answer:

\(x = 7\)