Question

TA is a tangent at A to the circle, centre O. Angle OAB = 50 degrees. Find the value of y,z, and t

Answer 1

Answer:

OB=OA[radii of same circle]

so,<OAB=<OBA[the angles opposite to equal sides are equal ]

angle OAB=angle OBA=50°

sum of the angles of triangle=180°

angle OBA+angle OAB+angle AOB=180°

50°+50°+y°=180°

100°+y°=180°

y°=180°-100°

y=80°

sum of the linear pair angle is equal to 180 degrees

angle OBA+angleABT=180°

50°+angleABT=180°

angle ABT = 180°-50°=130°

angle OAB+angle BAT=90°(TA is a tangent at A)

50°+angle BAT=90°

angle BAT(z°)=90°-50°=40°

sum of the angles of triangle is equal to 180 degrees

<ABT+<BAT+<ATB=180°

130°+40°+t°=180°

170°+t°=180°

t°=180°-170°

t°=10°