Question

1. 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. x = ______ determine the measure of ∠f. ∠f = ______

Explanation:

Step1: Apply angle - sum property of a triangle

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

Step2: Simplify the left - hand side

First, add the non - variable terms: \(40+76 + 71+x=180\), which gives \(187+x = 180\).

Step3: Solve for x

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

Step4: Find the measure of ∠F

Substitute \(x=-7\) into the expression for ∠F. ∠F=\(x + 71\). So, ∠F=\(-7+71 = 64^{\circ}\).

Answer:

\(x=-7\)
\(\angle F = 64^{\circ}\)