Question

two chords AB and CD intersect at right angles.If angle ABD=65 degree, find the measure of CAB

Answer 1

angle aoc =90
angle abd= angle ACD. angle on same segment
angle ACD = 65
in ∆ AOC
angle aoc + angle aco + angle cao= 180. angle sum property
90+65+ angle cao = 180
angle cao = 25
so angle cab = 25

Answer 2

given- a circle with chords AB and CD intersect at 90°. angle ABD= 65°.

to find- angle CAB

construction- join AD. name the point of intersections of two chords as P.

solution- now AD forms a chord that subtends angle ABD and angle ACD.
angle ABD = angle ACD
[angle in the same segment of a circle are equal]
now in ∆ACP,
angle ACP=65°, angle APC=90°
so,ACP+APC+CAP = 180° (angle sum property)
65°+90°+CAP= 180°
155°+CAP=180°
CAP=180°-155°
CAP=25°
or CAB=25°