If the measure of the tangent-chord angle is 74 degrees, then what is the measure of the intercepted arc inside the angle?

An angle formed by a tangent line and a chord is a special case of an inscribed angle. The formula is the same however.

The measure of an inscribed angle is half that of the measure of the interecpted arc. That means the measure of the subtended arc is twice that of the measure of the inscribed angle or 2*74 = 148°.

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Lanuel Lanuel · Answer 2 · 2022-02-24T10:58:12+01:00

The intercepted arc inside the angle is equal to 148 degrees.

Given the following data:

Tangent-chord angle = 74 degrees.

What is an inscribed angle?

An inscribed angle can be defined as an angle that is typically formed by a chord and a tangent line.

Based on trigonometry, the measure of an inscribed angle is generally equal to half of the measure of an intercepted arc. This ultimately implies that, the measure of the subtended arc is double (twice) the measure of the inscribed angle.

Mathematically, the intercepted arc inside the angle is given by:

[tex]I = 2 \times 74[/tex]

I = 148 degrees.

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