Question

please help me, I'm stuck on the second one. ​Also for i) i got angle ABD because angles in a semicircle measures 90 degree and OAX because the angle between the tangent and a radius is 90 degrees

Answer 1

i)

• DA is diameter and AX is tangent to circle

Your answer is correct

• m∠ABD = 90°, m∠DAX = 90°

ii)

Given m∠BAX = 42° and ∠DAB is complementary with BAX ⇒

• m∠DAB = 90° - 42° = 48°

DC = BC ⇒ intercepted arcs are same ⇒

• ∠CDB = ∠BDC

mDC = mCB ⇒ mDCB = ∠DAB = 48° ⇒

• m∠CDB = m∠BDC = 1/2*48 = 24°

iii)

∠CBA

∠CBA is supplementary with ∠ADC as opposite angles of cyclic quadrilateral (∠ADB = ∠BAX = 42°)

• m∠ADC = m∠ADB + m∠CDB = 42° + 24° = 68°
• m∠CBA = 180° - m∠ADC = 180° - 68° = 112°

∠BAE

EA║CB and AB is transversal ⇒ CBA and BAE are supplementary angles:

• m∠BAE = 180° - 112° = 68°

∠DCE

• ∠DCE = ∠DCB - ∠BCE

• m∠DCB = 180° - m∠DAB = 180° - 48° = 132°
• m∠BCE = 180° - m∠BAE = 180° - 68° = 112°
• ∠DCE = 132° - 112° = 20°