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Use the diagram to solve for the value of x. A. x 18° 13x) B. x 12° C. x 36° D. x 72° 720 O A

Use the diagram to solve for the value of x. A. x 18° 13x) B. x 12° C. x 36° D. x 72° 720 O A

Algebra and Trigonometry (6th Edition)
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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Question
**Use the diagram to solve for the value of x.** **Options:** A. \( x = 18^\circ \) B. \( x = 12^\circ \) C. \( x = 36^\circ \) D. \( x = 72^\circ \) (O) A \ ( ) B \ ( ) C \ ( ) D **Diagram Description:** The diagram is a triangle with the following specifications: - One angle is marked as \( 72^\circ \). - A second angle, opposite the first, is marked as \( (3x)^\circ \). - The third angle is unmarked and is to be determined. - Two sides of the triangle are marked as equal (indicated by hatch marks), making it an isosceles triangle. **Explanation:** To solve for the value of \( x \), you need to apply the properties of the isosceles triangle and the fact that the sum of the angles in any triangle is \( 180^\circ \). Since it is an isosceles triangle and one of the angles is \( 72^\circ \), the base angles (one of which is \( 3x \)) are equal. This allows us to set up an equation to solve for \( x \).
Transcribed Image Text:**Use the diagram to solve for the value of x.** **Options:** A. \( x = 18^\circ \) B. \( x = 12^\circ \) C. \( x = 36^\circ \) D. \( x = 72^\circ \) (O) A \ ( ) B \ ( ) C \ ( ) D **Diagram Description:** The diagram is a triangle with the following specifications: - One angle is marked as \( 72^\circ \). - A second angle, opposite the first, is marked as \( (3x)^\circ \). - The third angle is unmarked and is to be determined. - Two sides of the triangle are marked as equal (indicated by hatch marks), making it an isosceles triangle. **Explanation:** To solve for the value of \( x \), you need to apply the properties of the isosceles triangle and the fact that the sum of the angles in any triangle is \( 180^\circ \). Since it is an isosceles triangle and one of the angles is \( 72^\circ \), the base angles (one of which is \( 3x \)) are equal. This allows us to set up an equation to solve for \( x \).
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