Question

Find the lettered angles in each of the following.

( where a point o is given , it is the centre of the circle) .​

Answer 1

t and u are supplementary as opposite angles of a cyclic quadrilateral.

• t = 180 - (81 + 53) = 46
• u = 180 - t = 180 - 46 = 134

v and w are equal as opposite angles to equal sides.

• v = w = 1/2(180 - u) = 1/2(180 - 134) = 23

Answer 2

t=46°

u=134°

v=23°

w=23°

Answer:

Solution given;

v=w [base angle of triangle]

<SPQ+<SRQ=180°[sum of opposite angle of a cyclic quadrilateral is 180°]

81+v+53+w=180°

134°+v+v=180°

2v=180°-134°

v=46/2

v=23°

w=v=23°

In triangle ∆ PQR

v+w+u=180°[sum of interior angle of a triangle]

23+23+u=180°

u=180°-46°

u=134°

again

In triangle ∆ PSR

t+81+53=180°

t=180°-134°

t=46°