Question

12 directions - use the diagram to find the following measures: a) triangle angle sum equation = b) value of x = degrees

Explanation:

Step1: Recall angle - sum property

The sum of interior angles of a triangle is 180°. So for triangle ABC, the equation is \(x + 27+82=180\).

Step2: Solve for x

First, simplify the left - hand side: \(x+(27 + 82)=x + 109\). Then, we have the equation \(x+109 = 180\). Subtract 109 from both sides: \(x=180 - 109\). So \(x = 71\).

Answer:

a) \(x + 27+82=180\)
b) 71