inequalities in one triangle; triangle inequality
use the figure at the right to determine the relationship between
the measures of the given angles.
1. ( mangle qrw )____( mangle rwq ) 2. ( mangle rtw )____( mangle twr )
3. ( mangle rst )____( mangle trs ) 4. ( mangle wqr )____( mangle qrw )

Question

Accepted Answer

# Explanation: ## Step1: Recall the triangle - inequality theorem (angle - side relationship) In a triangle, the larger side is opposite the larger angle. ## Step2: Analyze $ \triangle QRW$ In $ \triangle QRW$, $QW = 45$, $QR=47$. Since $QR>QW$, the angle opposite $QR$ ($ \angle RWQ$) and the angle opposite $QW$ ($ \angle QRW$). So $m\angle QRW RW$, the angle opposite $RT$ ($ \angle TWR$) and the angle opposite $RW$ ($ \angle RTW$). So $m\angle RTWRT$, the angle opposite $RS$ ($ \angle TRS$) and the angle opposite $RT$ ($ \angle RST$). So $m\angle RSTRW$, the angle opposite $QW$ ($ \angle QRW$) and the angle opposite $RW$ ($ \angle WQR$). So $m\angle WQR>m\angle QRW$ # Answer: 1. $m\angle QRWm\angle QRW$

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QUESTION IMAGE

Question

Explanation:

Step1: Recall the triangle - inequality theorem (angle - side relationship)

Step2: Analyze \( \triangle QRW\)

Step3: Analyze \( \triangle RTW\)

Step4: Analyze \( \triangle RST\)

Step5: Analyze \( \triangle QWR\)

Answer: