Question

1. find the value of x find the m∠ijh

Explanation:

Step1: Use the exterior angle theorem

The exterior angle theorem states that an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles.
So, \(6x + 4+5x + 2=116\)

Step2: Simplify the left - hand side of the equation

Combine like terms: \((6x+5x)+(4 + 2)=116\), which gives \(11x+6 = 116\)

Step3: Solve for \(x\)

Subtract 6 from both sides: \(11x=116 - 6\), so \(11x=110\)
Divide both sides by 11: \(x=\frac{110}{11}=10\)

Step4: Find \(m\angle IJH\)

Since \(\angle IJH\) and the \(116^{\circ}\) angle are supplementary (they form a linear pair), \(m\angle IJH=180^{\circ}-116^{\circ}=64^{\circ}\)

Answer:

\(x = 10\)
\(m\angle IJH=64^{\circ}\)