Question

ABCD is a cyclic quadrilateral and AB is the diameter of the circle. If ∠CAB = 48 °, then what is the value (in degrees) of ∠ADC?

Answer 1

Solution :-

ABCD is a cyclic quadrilateral and AB is the diameter of a circle .

ΔACB lie in the semicircle

Therefore,

ΔACB = 90°

[ Triangle that lie in the semicircle so it makes angle of 90° ]

In ΔABC

By using Angle sum property ,

ΔABC + ΔACB + ΔCAB = 180°

Put the required values,

ΔABC + 90° + 48° = 180°

ΔABC + 138° = 180°

ΔABC = 180° - 138°

ΔABC = 42°

Now,

In cyclic quadrilateral ABCD,

ΔADC + ΔABC = 180°

[ The sum of opposite angles of cyclic quadrilateral is 180° ]

Put the required values,

ΔADC + 42° = 180°

ΔADC = 180° - 42°

ΔADC = 138°

Hence, The value of ΔADC = 138° $.$

Answer 2

Step-by-step explanation:

${ \huge{ \green{ \underline{ \mathfrak{given:}}}}} \\ \\ { \red{ \boxed{ \sf{∠CAB = 48⁰}}}} \: \: {\pink {\sf {and}}} \: \: { \blue{ \boxed{ \sf{∠ACB = 90⁰}}}} \\ \\ { \large{ \orange{☆ \boxed { \sf{Sum \: \: of \: \: all \: \: angles \: \: of \: \: Triangles \: = 180⁰}}}}} \\ \\ { \huge {\mathfrak{ \purple{ \underline { now:}}}}} \\ \\ \sf :→∠ABC + ∠BCA + ∠CAB = 180 \\ { \pink {\sf{ :→48⁰ + ∠ABC + 90⁰ = 180}}} \\ { \green{ \sf{:→∠ABC = 180⁰ - 138⁰}}} \\ { \red {\sf{:→∠ABC = 42⁰}}} \\ \\{ \large{ \blue{☆ \boxed{ \sf {Sum \: \: of \: \: opposite \: \: \: angles \: \: of \: \: \: cyclic \: \: quadrilateral = 180⁰}}}}} \\ \\ { \large{ \mathfrak{ \pink{ \underline{According \: \: to \: \: question:}}}}} \\ \\{ \red{ \sf {:→∠ACD + ∠ABC = 180⁰}}} \\ { \green{ \sf{:→∠ADC = 180⁰ - 42⁰}}} \\ { \large{ \purple{:→ \boxed{ \sf{∠ADC = 138⁰ \: \: Ans}}}}}$