The sum of the measures of the angles of any triangle is 180^∘ . In triangle A B C, the measure

Name: Problem 50, Chapter 7: Beginning and Intermediate Algebra
Uploaded: 2022-02-16T23:23:23-08:00
Duration: 1 min 34 s
Channel: Rylie Howey
Description: The sum of the measures of the angles of any triangle is 180^∘ . In triangle A B C, the measure of angle A is 141^∘ greater than the measure of angle B. The measure of angle B is the same as the measure of angle C . Find the measure of each angle.

step 1 Already we're talking about triangle A, B, C, and so we're going to have each of our angles here

Question

The sum of the measures of the angles of any triangle is $180^{\circ} .$ In triangle $A B C,$ the measure of angle $A$ is $141^{\circ}$ greater than the measure of angle $B$. The measure of angle $B$ is the same as the measure of angle $C .$ Find the measure of each angle.

   The sum of the measures of the angles of any triangle is $180^{\circ} .$ In triangle $A B C,$ the measure of angle $A$ is $141^{\circ}$ greater than the measure of angle $B$. The measure of angle $B$ is the same as the measure of angle $C .$ Find the measure of each angle.

Beginning and Intermediate Algebra

Margaret L. Lial,… 7th Edition

Chapter 7, Problem 50

Instant Answer

Solved by Expert Rylie Howey

02/16/2022

Step 1

According to the problem, the measure of angle $A$ is $141^{\circ}$ greater than the measure of angle $B$, so we can express the measure of angle $A$ as $x + 141^{\circ}$. Also, the measure of angle $B$ is the same as the measure of angle $C$, so the measure of Show more…

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The sum of the measures of the angles of any triangle is $180^{\circ} .$ In triangle $A B C,$ the measure of angle $A$ is $141^{\circ}$ greater than the measure of angle $B$. The measure of angle $B$ is the same as the measure of angle $C .$ Find the measure of each angle.

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Key Concepts

Algebraic Equation Solving in Geometry

This concept involves translating the relationships between geometric elements, such as angle differences or equalities, into algebraic equations. Using techniques like variable substitution and solving linear equations, one can determine precise values for unknown angles in a triangle.

Triangle Angle Sum Theorem

This fundamental principle in geometry states that the sum of the interior angles of any triangle is always 180 degrees. It is a key property used to determine unknown angle measures by setting up an equation based on the known relationships among the angles.

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