Inscribed Angles and Arcs — Practice Geometry Questions - dummies

Inscribed Angles and Arcs — Practice Geometry Questions

By Allen Ma, Amber Kuang

In geometry, when you have an inscribed angle on a circle, the measure of the inscribed angle and the length of the intercepted arc are related.

An inscribed angle is equal to half of the intercepted arc.

The following practice questions ask you to find the measure of an inscribed arc and an inscribed angle.

Practice questions

  1. Equilateral triangle

    image0.png

    is inscribed in Circle O.

    image1.png

    Find the missing arc

    image2.png

  2. In Circle O,

    image3.png

    is a right triangle with diameter

    image4.png

    as the hypotenuse.

    image5.png

    If

    image6.png

    and OR = 20, find

    image7.png

Answers and explanations

  1. 120 degrees

    image8.png

    is equilateral, which means all sides of the triangle are equal. This also means that

    image9.png

  2. 60 degrees

    The inscribed angle of a circle is half the measure of the intercepted arc:

    image10.png