Question

question 5.a zach is building a fence around a property shaped like a triangle. he measures ∠d and ∠e using a transit and needs to calculate ∠f manually. determine the value of x.

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. So, \(40^{\circ}+76^{\circ}+(x + 71)^{\circ}=180^{\circ}\).

Step2: Simplify the left - hand side

\(40 + 76+x + 71=180\), which simplifies to \(x+187 = 180\).

Step3: Solve for x

Subtract 187 from both sides: \(x=180 - 187=-7\).

Answer:

\(x=-7\)