Questions: (a) An angle measures 80°. What is the measure of its supplement? (b) An angle measures 29°. What is the measure of its complement?

Transcript text: (a) An angle measures $80^{\circ}$. What is the measure of its supplement? (b) An angle measures $29^{\circ}$. What is the measure of its complement?

Solution

Solution Steps

Finding the Complement and Supplement of an Angle

Given an angle $x = 80^\circ$, we are to find its complement and supplement.

Step 1: Find the Complement

The formula to find the complement of an angle $x$ is: \[ ext{Complement of } x = 90^\circ - x \] Substituting the given value of $x$, we get: \[ ext{Complement of } 80^\circ = 90^\circ - 80^\circ = 10^\circ \]

Step 2: Find the Supplement

The formula to find the supplement of an angle $x$ is: \[ ext{Supplement of } x = 180^\circ - x \] Substituting the given value of $x$, we get: \[ ext{Supplement of } 80^\circ = 180^\circ - 80^\circ = 100^\circ \]

Final Answer:

The complement of the angle $x = 80^\circ$ is 10^\circ, and the supplement is 100^\circ.

Finding the Complement and Supplement of an Angle

Given an angle $x = 29^\circ$, we are to find its complement and supplement.

Step 1: Find the Complement

The formula to find the complement of an angle $x$ is: \[ ext{Complement of } x = 90^\circ - x \] Substituting the given value of $x$, we get: \[ ext{Complement of } 29^\circ = 90^\circ - 29^\circ = 61^\circ \]

Step 2: Find the Supplement

The formula to find the supplement of an angle $x$ is: \[ ext{Supplement of } x = 180^\circ - x \] Substituting the given value of $x$, we get: \[ ext{Supplement of } 29^\circ = 180^\circ - 29^\circ = 151^\circ \]

Final Answer:

The complement of the angle $x = 29^\circ$ is 61^\circ, and the supplement is 151^\circ.

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