Question

ABCDE is a cyclic Pentagon.AB=BC and AC is the diameter of the circle. If ANGLE AED=118°, then find the value of angle DAB

Answer 1

Answer:

∠DAB is 73°

Step-by-step explanation:

Given ABCDE is a cyclic Pentagon. AB=BC and AC is the diameter of the circle. If ∠AED=118°. we have to find ∠DAB.

∠ADC and ∠ABC are angles subtended in the semicircle ∴ each 90°

Now, AB=BC ⇒ ∠BAC=∠BCA

By angle sum property in ΔABC

∠BAC+∠ABC+∠BCA=180°

⇒ 2∠BAC+90°=180°

⇒∠BAC=45°

AEDC is a cyclic quadrilateral ⇒∠AED+∠ACD=180°

⇒ 118°+∠ACD=180° ⇒ ∠ACD=62°

In ΔADC, by angle sum property

∠DAC+∠ADC+∠ACD=180°

⇒ ∠DAC+62°+90°=180°

⇒ ∠DAC=28°

Hence, ∠DAB=28°+45°=73°

Answer 2

Step-by-step explanation:

this is the answer to the question