Question

what is the value of z?
diagram of a triangle with an exterior angle: interior angles labeled (2z + 44^circ), (34^circ); exterior angle labeled (9z + 46^circ)
write your answer as an integer or as a decimal rounded to the nearest tenth.
( z = square^circ )

Explanation:

Step1: Use the 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 $9z + 46=(2z + 44)+34$.

Step2: Simplify the right - hand side

Simplify $(2z + 44)+34$: $2z+44 + 34=2z + 78$. So the equation becomes $9z+46 = 2z+78$.

Step3: Subtract 2z from both sides

Subtract $2z$ from each side of the equation: $9z-2z + 46=2z-2z + 78$, which simplifies to $7z+46 = 78$.

Step4: Subtract 46 from both sides

Subtract 46 from each side: $7z+46 - 46=78 - 46$, so $7z=32$.

Step5: Solve for z

Divide both sides by 7: $z=\frac{32}{7}\approx4.6$ (rounded to the nearest tenth).

Answer:

$4.6$