Question

2-5 additional practice parallel lines and triangle angle sums for exercises 1–6, find the value of each variable.

Explanation:

Exercise 1

Step1: Recall triangle angle sum

The sum of angles in a triangle is \(180^\circ\). So, \(92^\circ + 63^\circ + x^\circ = 180^\circ\).

Step2: Calculate sum of known angles

\(92 + 63 = 155\). So, \(155 + x = 180\).

Step3: Solve for \(x\)

Subtract 155 from both sides: \(x = 180 - 155 = 25\).

Step1: Recall triangle angle sum

Sum of angles in a triangle is \(180^\circ\). So, \(20^\circ + 87^\circ + x^\circ = 180^\circ\).

Step2: Calculate sum of known angles

\(20 + 87 = 107\). So, \(107 + x = 180\).

Step3: Solve for \(x\)

Subtract 107 from both sides: \(x = 180 - 107 = 73\).

Step1: Recall triangle angle sum

Sum of angles in a triangle is \(180^\circ\). So, \(80^\circ + 40^\circ + x^\circ = 180^\circ\).

Step2: Calculate sum of known angles

\(80 + 40 = 120\). So, \(120 + x = 180\).

Step3: Solve for \(x\)

Subtract 120 from both sides: \(x = 180 - 120 = 60\).

Answer:

\(x = 25\)

Exercise 2