Given: AB=108^∘, CD=62^∘ Find: ∠AXB and ∠Y CAN'T COPY THE GRAPH

Name: Problem 7, Chapter 10: Geometry for Enjoyment and Challenge
Uploaded: 2021-05-26T20:51:54-08:00
Duration: 3 min 28 s
Channel: Erika Bustos
Description: Given: AB=108^∘, CD=62^∘ Find: ∠AXB and ∠Y CAN'T COPY THE GRAPH

step 1 We're given the following circle, and we're given that arc AB is equal to 108 degrees, and we're

Given: AB=108^∘, CD=62^∘ Find: ∠AXB and ∠Y...

$$\begin{aligned}&\text { Given: } \widehat{\mathrm{AB}}=108^{\circ}, \widehat{\mathrm{CD}}=62^{\circ}\\
&\text { Find: } \angle \mathrm{AXB} \text { and } \angle \mathrm{Y}\end{aligned}$$
CAN'T COPY THE GRAPH

Key Concepts

Arc Measurement

An arc on a circle is a portion of its circumference and its measure is given in degrees. Understanding how to interpret and use arc measurements is essential when relating them to angles, whether they are central angles or inscribed angles, since these angles correspond directly to the arcs they subtend.

Inscribed Angle Theorem

The inscribed angle theorem states that an angle formed by two chords in a circle with the vertex on the circle is half the measure of its intercepted arc. This theorem is crucial when calculating angles that depend on the corresponding arc measures, as it allows you to convert between an arc’s measure and the angle that intercepts that arc.

Angles Formed by Intersecting Chords

When two chords intersect inside a circle, the measure of an angle formed at the intersection is equal to half the sum of the measures of the arcs intercepted by that angle and its vertical opposite. This key concept is often used to determine unknown angles in circle geometry when various arc measurements are given.

Angles Formed Outside the Circle

Angles formed by two secants, a secant and a tangent, or two tangents that intersect outside a circle have a measure equal to half the difference of the measures of the intercepted arcs. This concept is important in problems where the vertex of the angle is located outside the circle, requiring a different approach compared to angles with vertices on or inside the circle.

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