Question

what is the correct classification for each given angle? drag and drop the answer into the box to match each angle. ∠rqu ∠squ ∠rqt acute right obtuse straight

Explanation:

Step1: Calculate ∠RQU

To find ∠RQU, we sum the angles between RQ and SQ, SQ and TQ, and TQ and UQ. So, ∠RQU = 19° + 71° + 18° = 108°. An obtuse angle is greater than 90° and less than 180°, so ∠RQU is obtuse.

Step2: Calculate ∠SQU

For ∠SQU, we sum the angles between SQ and TQ, and TQ and UQ. So, ∠SQU = 71° + 18° = 89°? Wait, no, wait: Wait, RQ to SQ is 19°, SQ to TQ is 71°, TQ to UQ is 18°. Wait, maybe I misread. Wait, ∠SQU: from SQ to UQ. So SQ to TQ is 71°, TQ to UQ is 18°, so 71 + 18 = 89? Wait, no, wait, maybe the angles are RQ to SQ: 19°, SQ to TQ: 71°, TQ to UQ: 18°, and then QV is another ray. Wait, maybe I made a mistake. Wait, let's re - examine. The angle between RQ and SQ is 19°, SQ and TQ is 71°, TQ and UQ is 18°. So ∠SQU: SQ to UQ. So that's 71°+18° = 89°? But 89° is acute? Wait, no, wait, maybe the sum is 19 + 71+18? Wait, no, ∠RQU is from RQ to UQ. So RQ to SQ (19°), SQ to TQ (71°), TQ to UQ (18°). So 19 + 71+18 = 108°, which is obtuse. Then ∠SQU: SQ to UQ. So SQ to TQ (71°) and TQ to UQ (18°), so 71 + 18 = 89°? Wait, no, 71+18 = 89? Wait, 71 + 18 is 89? Wait, 70+18 = 88, plus 1 is 89. So 89° is acute? Wait, no, acute is less than 90°, right angle is 90°, obtuse is more than 90° and less than 180°. Wait, maybe I miscalculated ∠SQU. Wait, maybe the angle between SQ and RQ is 19°, SQ and TQ is 71°, so RQ and TQ is 19 + 71=90°, which is a right angle. Then ∠RQT: RQ to TQ, 19 + 71 = 90°, so right angle. Then ∠SQU: SQ to UQ. SQ to TQ is 71°, TQ to UQ is 18°, so 71+18 = 89°? No, 71 + 18 is 89? Wait, 71+18 = 89? Wait, 70+18 = 88, 88 + 1=89. So 89° is acute? Wait, but maybe I made a mistake. Wait, let's start over.

First, recall angle classifications:

• Acute: less than 90°
• Right: equal to 90°
• Obtuse: greater than 90° and less than 180°
• Straight: 180°

Now, let's find each angle:

1. ∠RQT: The angle between RQ and TQ. The angle between RQ and SQ is 19°, and between SQ and TQ is 71°. So ∠RQT = 19°+71° = 90°. So ∠RQT is a right angle.

1. ∠SQU: The angle between SQ and UQ. The angle between SQ and TQ is 71°, and between TQ and UQ is 18°. So ∠SQU = 71°+18° = 89°? Wait, no, 71 + 18=89? Wait, 71+18 = 89? Wait, 70+18 = 88, 88 + 1=89. So 89° is less than 90°, so acute? Wait, but maybe I misread the diagram. Wait, maybe the angle between TQ and UQ is 18°, SQ and TQ is 71°, so SQ to UQ is 71 + 18=89°, which is acute.

1. ∠RQU: The angle between RQ and UQ. We can calculate it as ∠RQT+∠TQU. ∠RQT is 90°, ∠TQU is 18°, so 90 + 18=108°. 108° is greater than 90° and less than 180°, so obtuse.

Answer:

• ∠RQU: obtuse
• ∠SQU: acute
• ∠RQT: right