Elementary Geometry For College Students, 7e
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
Related questions
Question
![**Find the unknown angle measures.**
This image contains a triangle labeled as \( \triangle GHJ \). There is one known angle measure provided: \( \angle H = 64^\circ \).
The diagram shows:
- A triangle with vertices labeled as G, H, and J.
- The angle at vertex H is labeled as \(64^\circ\).
Task:
- Determine the measures of the unknown angles \( \angle G \) and \( \angle J \).
Below the triangle, there are input boxes for recording the calculated measures:
\( m\angle G = \_\_\_^\circ \)
\( m\angle J = \_\_\_^\circ \)
To find the unknown angles:
- Use the fact that the sum of the interior angles of a triangle is always \(180^\circ\).
- Calculate the remaining angles using the equation:
\[
m\angle G + m\angle J + 64^\circ = 180^\circ
\]
Solve for \( m\angle G \) and \( m\angle J \) using the equation above.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F43eb41af-d84b-40c1-ba80-6ea778a40d08%2F6ab1306f-7ec7-4e64-b058-d6c54aab4851%2Fboxmlti_processed.png&w=3840&q=75)
Transcribed Image Text:**Find the unknown angle measures.**
This image contains a triangle labeled as \( \triangle GHJ \). There is one known angle measure provided: \( \angle H = 64^\circ \).
The diagram shows:
- A triangle with vertices labeled as G, H, and J.
- The angle at vertex H is labeled as \(64^\circ\).
Task:
- Determine the measures of the unknown angles \( \angle G \) and \( \angle J \).
Below the triangle, there are input boxes for recording the calculated measures:
\( m\angle G = \_\_\_^\circ \)
\( m\angle J = \_\_\_^\circ \)
To find the unknown angles:
- Use the fact that the sum of the interior angles of a triangle is always \(180^\circ\).
- Calculate the remaining angles using the equation:
\[
m\angle G + m\angle J + 64^\circ = 180^\circ
\]
Solve for \( m\angle G \) and \( m\angle J \) using the equation above.
![**Find the unknown angle measures.**
The diagram shown is a triangle labeled as ∆QNP.
- **Angle N** is marked as 132°.
- Sides QN and NP are marked with a small line, indicating they are of equal length.
Below the diagram, there are fields to enter the measures of angles P and Q:
- m∠P = [ ]
- m∠Q = [ ]
**Explanation:**
In this isosceles triangle ∆QNP, angles P and Q are equal because the sides opposite them (QN and NP) are equal. The measure of angle N is given as 132°.
To find angles P and Q, you can use the triangle angle sum property, which states that the sum of the angles in a triangle is always 180°. The calculation is:
180° - 132° = 48°
Since angles Q and P are equal:
m∠Q = m∠P = 48° / 2 = 24° each.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F43eb41af-d84b-40c1-ba80-6ea778a40d08%2F6ab1306f-7ec7-4e64-b058-d6c54aab4851%2Filsw4zv_processed.png&w=3840&q=75)
Transcribed Image Text:**Find the unknown angle measures.**
The diagram shown is a triangle labeled as ∆QNP.
- **Angle N** is marked as 132°.
- Sides QN and NP are marked with a small line, indicating they are of equal length.
Below the diagram, there are fields to enter the measures of angles P and Q:
- m∠P = [ ]
- m∠Q = [ ]
**Explanation:**
In this isosceles triangle ∆QNP, angles P and Q are equal because the sides opposite them (QN and NP) are equal. The measure of angle N is given as 132°.
To find angles P and Q, you can use the triangle angle sum property, which states that the sum of the angles in a triangle is always 180°. The calculation is:
180° - 132° = 48°
Since angles Q and P are equal:
m∠Q = m∠P = 48° / 2 = 24° each.
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