Question

question 7 (5 points)
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in the figure, find ( mangle rst ) if ( mangle rsu = 81^{circ} ) and ( mangle ust = 18^{circ} ).
a) ( 99^{circ} )
b) ( 63^{circ} )
c) ( 109^{circ} )
d) ( 81^{circ} )

Explanation:

Step1: Identify angle addition

To find \( m\angle RST \), we use the angle addition postulate, which states that if a ray is inside an angle, the sum of the two smaller angles equals the larger angle. So, \( m\angle RST = m\angle RSU + m\angle UST \).

Step2: Substitute the given values

We know \( m\angle RSU = 81^\circ \) and \( m\angle UST = 18^\circ \). Substituting these into the formula: \( m\angle RST = 81^\circ + 18^\circ \).

Step3: Calculate the sum

\( 81^\circ + 18^\circ = 99^\circ \).

Answer:

A) \( 99^\circ \)