Certainly! Let's solve the given problem step by step:
1. Understand the Problem: We are given that the sum of two vertically opposite angles is 166°. We need to determine the measure of each angle.
2. Concept of Vertically Opposite Angles: Vertically opposite angles are equal. When two lines intersect, they form two pairs of vertically opposite angles. For instance, if two lines intersect at point O, forming angles A, B, C, and D, then angle A is vertically opposite and equal to angle C, and angle B is vertically opposite and equal to angle D.
3. Given Information: The sum of the two vertically opposite angles is 166°. Let [tex]\( x \)[/tex] be the measure of one of these angles. Since the angles are equal:
[tex]\[
x + x = 166°
\][/tex]
4. Set up the Equation:
[tex]\[
2x = 166°
\][/tex]
5. Solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{166°}{2}
\][/tex]
[tex]\[
x = 83°
\][/tex]
6. Conclusion: Therefore, each of the vertically opposite angles is 83°.
Hence, the measure of each angle is [tex]\( 83° \)[/tex].
