One of the resulting angles that would be formed if ray QT is the angle bisector of angle RQS is: 23°.
What is an Angle Bisector?
The line segment or ray that bisects an angle is called the angle bisector. It means the angle it bisects is divided into two equal angles.
Angle PQS is a straight line angle which is equal to 180 degrees.
Angle PQR = 3x + 5
Angle RQS = x + 3
Therefore, we would have the equation:
Angle PQR + angle RQS = 180
3x + 5 + x + 3 = 180
Add like terms
4x + 8 = 180
4x = 180 - 8
4x = 172
Divide both sides by 4
4x/4 = 172/4
x = 43
Angle PQR = 3x + 5 = 3(43) + 5 = 134°
Angle RQS = x + 3 = 43 + 3 = 46°.
Ray QT is an angle bisector of angle RQS. Half of angle RQS would be:
Half of m<RQS = 1/2(46)
Half of m<RQS = 23°
Therefore, one of the resulting angles that would be formed if ray QT is the angle bisector of angle RQS is: 23°.
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