Question

triangles finding an angle measure given extended triangles try again your answer is incorrect. find x. 45° x° 31° 110° x = explanation recheck

Explanation:

Step1: Use the property of vertical angles

Vertical angles are equal. So the angle adjacent to \(110^{\circ}\) inside the triangle is \(180 - 110=70^{\circ}\). Also, the angle opposite to \(31^{\circ}\) (due to vertical angles) is \(31^{\circ}\).

Step2: Apply the angle - sum property of a triangle

The sum of angles in a triangle is \(180^{\circ}\). Let's consider the triangle with angles \(45^{\circ}\), \(x^{\circ}\), \(70^{\circ}\) and the angle related to \(31^{\circ}\). Using the angle - sum formula for a triangle: \(45 + x+70=180 - 31\).
Simplify the right - hand side: \(180- 31 = 149\). Then the left - hand side: \(45+70+x=115 + x\).
Set up the equation \(115+x=149\).
Subtract 115 from both sides: \(x=149 - 115\).

Answer:

\(x = 34\)