Question

Find the value of x in the diagram shown below.

can someone help me here (show the solution)​

Answer 1

a) ∡ADC = 270°

b) ∠DAE = 38°

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

a) arc ADC = 270°

b) angle DAE = 38°

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.

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a)

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

Arc ADC = 2 × 135° = 270°

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b)

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

Angle DAE = 1/2 × 76° = 38°