SOLUTION TO LAST MONTH'S QUIZ
1. x = 33^{o}
2. y = 78^{o}
3. z = 60^{o}
Notes.
angle BAP = 33^{o} (angles of tr. BAP)
So x = 33^{o} (alt. seg.) *
angle BAQ = 78^{o} (angles of tr.BAQ)
So y = 78^{o} (alt. seg.) *
So x + y + 42 + 27 = 180 (angles of tr.PAQ)
So quad.PAQT is cyclic (opp. angles supplementary)
So angle ATQ = angle APQ = 42^{o} (same seg.) **
So z = 60^{o} (angles of tr.)
* "The angle a tangent makes with a chord equals the angle in the alternate segment"
** "Angles in the same segment are equal"
