Find the measure of zC. C 73 87 A B.

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Find the measurement of C
**Finding the Measure of Angle \( \angle C \)**

In this problem, you are presented with a triangle \( \triangle ABC \) and need to determine the measure of angle \( \angle C \).

From the diagram:
- Angle \( \angle A \) measures 87 degrees.
- Angle \( \angle B \) measures 73 degrees.

To find \( \angle C \), you need to use the fact that the sum of the interior angles of a triangle is always 180 degrees. This can be stated as: 
\[ \angle A + \angle B + \angle C = 180^\circ \]

Given:
\[ \angle A = 87^\circ \]
\[ \angle B = 73^\circ \]

Substituting the known values into the equation:
\[ 87^\circ + 73^\circ + \angle C = 180^\circ \]

Combining the measures of angles \( \angle A \) and \( \angle B \):
\[ 160^\circ + \angle C = 180^\circ \]

To isolate \( \angle C \):
\[ \angle C = 180^\circ - 160^\circ \]
\[ \angle C = 20^\circ \]

Therefore, the measure of \( \angle C \) is 20 degrees.
Transcribed Image Text:**Finding the Measure of Angle \( \angle C \)** In this problem, you are presented with a triangle \( \triangle ABC \) and need to determine the measure of angle \( \angle C \). From the diagram: - Angle \( \angle A \) measures 87 degrees. - Angle \( \angle B \) measures 73 degrees. To find \( \angle C \), you need to use the fact that the sum of the interior angles of a triangle is always 180 degrees. This can be stated as: \[ \angle A + \angle B + \angle C = 180^\circ \] Given: \[ \angle A = 87^\circ \] \[ \angle B = 73^\circ \] Substituting the known values into the equation: \[ 87^\circ + 73^\circ + \angle C = 180^\circ \] Combining the measures of angles \( \angle A \) and \( \angle B \): \[ 160^\circ + \angle C = 180^\circ \] To isolate \( \angle C \): \[ \angle C = 180^\circ - 160^\circ \] \[ \angle C = 20^\circ \] Therefore, the measure of \( \angle C \) is 20 degrees.
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