Question

Find the value of x in the diagram shown below.

Answer 1

Answer:

a) ∡ADC = 270°

b) ∠DAE = 38°

Step-by-step explanation:

Using Inscribed Angle Theorem :

• ∡ADC = 2 x ∠ABC
• ∡ADC = 2 x 135°
• ∡ADC = 270°

Similarly :

• ∠DAE = 1/2 x ∡DE
• ∠DAE = 1/2 x 76°
• ∠DAE = 38°

Answer 2

Answer:

  a) arc ADC = 270°

  b) angle DAE = 38°

Step-by-step explanation:

An inscribed angle is half the measure of the arc it subtends. The converse of this is that the arc is twice the measure of the inscribed angle that subtends it.

__

a)

Arc ADC is twice the measure of inscribed angle ABC, so is ...

  Arc ADC = 2 × 135° = 270°

__

b)

Angle DAE is half the measure of the arc it subtends, so is ...

  Angle DAE = 1/2 × 76° = 38°