Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN: 9781337614085
Author: Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher: Cengage,
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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.
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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.
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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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