In the figure above, PQR is a straight line segment, PQ = QT. Triangle PQT is an isosceles triangle, ?SQR is 75\(^{\circ}\) and ?QPT is 25\(^{\circ}\). Calc...
Question 1 Report
In the figure above, PQR is a straight line segment, PQ = QT. Triangle PQT is an isosceles triangle, ?SQR is 75\(^{\circ}\) and ?QPT is 25\(^{\circ}\). Calculate the value of ?RST.
Answer Details
In ? PQT,
?PTQ = 25(base ?s of isosceles ?)
In ? QSR,
?RQS = ?QPT + ?QTP
(Extr = sum of interior opposite ?s)
?RQS = 25 + 25
= 50
Also in ? QSR,
75 + ?RQS + ?QSR = 180
(sum of ?s of ?)
?75 + 50 + ?QSR = 180
125 + ?QSR = 180
?QSR = 180 - 125
?QSR = 55
But ?QSR and ?RST are the same
?RST = 55
?PTQ = 25(base ?s of isosceles ?)
In ? QSR,
?RQS = ?QPT + ?QTP
(Extr = sum of interior opposite ?s)
?RQS = 25 + 25
= 50
Also in ? QSR,
75 + ?RQS + ?QSR = 180
(sum of ?s of ?)
?75 + 50 + ?QSR = 180
125 + ?QSR = 180
?QSR = 180 - 125
?QSR = 55
But ?QSR and ?RST are the same
?RST = 55
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