TACHS Quiz: Angle Relationships

2 questions · exam conditions

0:00

Angle RelationshipsQuestion 1 of 2

Refer to the figure. Two chords $\overline{AB}$ and $\overline{CD}$ of a circle intersect inside the circle at point $P$ . Arc $AC$ (not containing $B$ or $D$ ) measures $84°$ and arc $BD$ (not containing $A$ or $C$ ) measures $46°$ . What is the measure of $\angle APC$ ?

$Question graphic$

19°

38°

65°

130°

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TACHS Quiz

TACHS Quiz: Angle Relationships

Practice Angle Relationships in TACHS with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Angle Relationships, giving you a quick way to practice the rules, question types, and explanations that matter most for TACHS.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

$19°$
$38°$
$65°$ (correct answer)
$130°$

Explanation: The measure of an angle formed by two chords intersecting inside a circle equals half the sum of the intercepted arcs:

\angle APC = \frac{1}{2}(84°+46°) = \frac{1}{2}(130°) = 65°

. (A)

19°

uses the external-angle formula (half the difference). (B)

38°

is half of

76°

, a miscalculation. (D)

130°

is the sum of arcs without halving.

Question 2

In the figure, $\overline{PA}$ is tangent to the circle at $A$ , and $\overline{PBC}$ is a secant passing through the circle, with $B$ closer to $P$ . If arc $AC$ (far arc, not containing $B$ ) $= 148°$ and arc $AB$ (near arc, not containing $C$ ) $= 62°$ , what is the measure of $\angle APC$ ?

$43°$ (correct answer)
$105°$
$86°$
$74°$

Explanation: The angle formed by a tangent and a secant from an external point equals half the difference of the intercepted arcs:

\angle APC = \frac{1}{2}(\text{far arc} - \text{near arc}) = \frac{1}{2}(148°-62°) = \frac{1}{2}(86°) = 43°

. (B)

105°

is half the sum. (C)

86°

is the difference without halving. (D)

74°

is half of

148°