### Understanding Angles in Geometry#### Question 9: Angle CalculationThe image contains two separate angular problems that involve calculating unknown angles in given geometrical configurations.**Left Diagram Explanation:**1. This diagram depicts three lines intersecting, forming angles at the point of intersection.2. 3. - One of the angles formed is labeled as \( 39^\circ \). - The angle adjacent to it on the straight line is labeled as \( ? \) (unknown).**Calculation Method:**To find the unknown angle \( ? \):Since the angles on a straight line sum up to \( 180^\circ \), we use the equation:\[39^\circ + ? = 180^\circ\]Rearranging to solve for \( ? \):\[? = 180^\circ - 39^\circ = 141^\circ\]Hence, the unknown angle \( ? \) is \( 141^\circ \).**Right Diagram Explanation:**1. This diagram shows a pair of intersecting lines, forming a set of four angles.2. 3. - Two of the angles formed are labeled as \( 30^\circ \) and \( 150^\circ \). - Another angle formed within the intersecting angles is labeled as \( 37^\circ \). - The angle adjacent to \( 37^\circ \) on the straight line is labeled as \( ? \) (unknown).**Calculation Method:**To find the unknown angle \( ? \):Since the angles on a straight line sum up to \( 180^\circ \), we use the equation:\[150^\circ + ? + 37^\circ + 30^\circ ? = 180^\circ\]Rearranging to solve for \( ? \):\[? = 180^\circ +150^\circ -37^\circ -30^\circ = 110^\circ\]Hence, the unknown angle \( ? \) is \( 110^\circ \).#### ConclusionUnderstanding how to calculate unknown angles in geometrical figures by utilizing the properties of adjacent angles on a straight line and the fact that the interior angles of intersecting lines sum up to \( 180^\circ \) is fundamental. In these problems, knowing basic angle properties allows for solving unknown angles effectively. ## Geometry Practice Problems### Problem 8**Diagram:**- This problem features a diagram with multiple lines intersecting.- A vertical line intersects a horizontal line, creating an angle.- The angle formed above the horizontal line by the vertical line is labeled \( 35^\circ \).- There is a diagonal line extending to the left from the intersection of the vertical line and the horizontal line.- Another angle is formed to the right of this diagonal line, below the horizontal line, which is labeled \( 39^\circ \).- The angle adjacent to the \( 35^\circ \) and \( 39^\circ \) angles is unknown (labeled as ?).**Objective:**- Determine the value of the unknown angle.### Problem 9**Diagram:**- This problem features a crossed line diagram.- A horizontal line crosses another horizontal line.- An obtuse angle is formed on the upper left side of the intersection, labeled \( 30^\circ \).- A diagonal line intersects the upper horizontal line and slopes downward to the right, forming an angle of \( 37^\circ \) with the lower horizontal line.- The angle adjacent to the \( 30^\circ \) and \( 37^\circ \) angles is unknown (labeled as ?).**Objective:**- Determine the value of the unknown angle.### Problem 10**Note:**- The content of Problem 10 is not visible within the provided image.**Objective:**- Based on the information provided, reference material may need to be consulted to complete Problem 10.

Answered: Image /qna-images/answer/f9dba9e6-dc00-4961-a24a-10394ce1f7c1.jpg

Answered: O File | DHPSCANS/Sum20o20Triangles0001…

O File | DHPSCANS/Sum20o20Triangles0001 pdf 9) 30° 150° 370 39°

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT