Question

Circle H is inscribed with quadrilateral D E F G. Angle E is 123 degrees. The measure of arc D E is 73 degrees. What is the measure of arc EF in circle H?

Answer 1

We know that

The inscribed angle = $\frac{1}{2}$ (arc comprising)

So,

∠E = $\frac{1}{2}$ (arc DGF)

∵ it is given that ∠E = 123°

∵ On substituting the value in the above equation, we get,

∠E = 123°

⇒ 123°  = $\frac{1}{2}$ (arc DGF)

⇒ arc DGF = 246°

Now, we find the measure of arc EF.

It is known that,

arc DGF + arc DE + arc EF = 360°

On substituting the values of the corresponding angles, we get,

(246 + 73 + arc EF)° = 360°

⇒ 319° + arc EF = 360°

⇒ arc EF = (360 - 319)°

⇒ arc EF = 41°

Ans) The measure of arc EF is 41°

Answer 2

Answer:

41 deg

Step-by-step explanation: