Question

1. in the diagram below, ( mangle tsv = 21^{circ} ) and ( mangle rsv = 48^{circ} ). determine ( mangle rst ).

(1) ( 27^{circ} )
(2) ( 42^{circ} )
(3) ( 69^{circ} )
(4) ( 132^{circ} )

Explanation:

Step1: Analyze the relationship between angles

From the diagram, we know that \(m\angle RSV=m\angle RST + m\angle TSV\). So, \(m\angle RST=m\angle RSV - m\angle TSV\).

Step2: Substitute the given values

Given \(m\angle TSV = 21^{\circ}\) and \(m\angle RSV=48^{\circ}\), substitute them into the formula: \(m\angle RST = 48^{\circ}-21^{\circ}\).

Step3: Calculate the result

\(48 - 21=27\), so \(m\angle RST = 27^{\circ}\).

Answer:

(1) \(27^{\circ}\)