Question

what is the value of x?

x=

Explanation:

Step1: Recall triangle angle sum

The sum of angles in a triangle is \(180^\circ\). So, \(96^\circ + 71^\circ + 5x^\circ = 180^\circ\).

Step2: Simplify the left - hand side

First, calculate \(96 + 71 = 167\). So the equation becomes \(167 + 5x = 180\).

Step3: Solve for \(x\)

Subtract 167 from both sides: \(5x = 180 - 167 = 13\). Then divide both sides by 5: \(x=\frac{13}{5}=2.6\)? Wait, no, wait, maybe I misread the angles. Wait, maybe the angles are \(96^\circ\), \(71^\circ\) and \(5x^\circ\)? Wait, no, maybe the angles are \(96^\circ\), \(7x^\circ\) and \(5x^\circ\)? Wait, the user's image: let me re - check. Oh, maybe the angles are \(96^\circ\), \(7x^\circ\) and \(5x^\circ\)? Wait, the original problem: the triangle has angles \(96^\circ\), \(7x^\circ\) and \(5x^\circ\)? Wait, the user's image shows "96°", "7x°" (maybe I misread earlier) and "5x°". Let's correct that.

Step1: Correct angle sum formula

Sum of angles in a triangle: \(96 + 7x+5x = 180\)

Step2: Combine like terms

\(96 + 12x = 180\)

Step3: Subtract 96 from both sides

\(12x = 180 - 96 = 84\)

Step4: Divide by 12

\(x=\frac{84}{12}=7\)

Answer:

\(7\)