Question

the diagram shows a triangle.
what is the value of x?
x = \boxed{}

Explanation:

Step1: Sum of triangle angles

The sum of angles in a triangle is $180^\circ$. Set up the equation:
$$79 + 34 + (29x + 9) = 180$$

Step2: Simplify left side

Add the constant terms:
$$79 + 34 + 9 + 29x = 180$$
$$122 + 29x = 180$$

Step3: Isolate the variable term

Subtract 122 from both sides:
$$29x = 180 - 122$$
$$29x = 58$$

Step4: Solve for x

Divide both sides by 29:
$$x = \frac{58}{29}$$
$$x = 2$$

Answer:

$x = 2$