Question

1-4: lesson quiz geometry with stat: section 301 (lms) 1-4: lesson quiz (lms graded) what is the measure of the vertex angle in the next triangle in the pat not to scale vertex angle =

Explanation:

Step1: Observe the pattern of base - angles

The base - angles of the given isosceles triangles are decreasing by 1° each time. The next base - angles will be 85° each.

Step2: Use the angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. Let the vertex angle be \(x\). We know that \(x + 2\times85^{\circ}=180^{\circ}\).

Step3: Solve for the vertex angle

\[

$$\begin{align*} x&=180^{\circ}- 2\times85^{\circ}\\ x&=180^{\circ}-170^{\circ}\\ x& = 10^{\circ} \end{align*}$$

\]

Answer:

10°