If O is the circumcentre lying inside the ΔDEF with value of ∠EOF

1.	If O is the circumcentre lying inside the ΔDEF with value of ∠EOF equal to 150°, find the measure of ∠D?1. 150° 2. 30° 3. 165° 4. 75°
Answer» Correct Answer - Option 4 : 75° Given: O is the circumcentre inside the ΔDEF. ∠EOF = 150° Concepts used: The measure of the angle formed with the given base at circumcentre = 2 × vertex angle formed opposite to the same base Calculation: ⇒ ∠EOF = 2 × ∠D ⇒ 150° = 2 × ∠D ⇒ ∠D = 150°/2 ⇒ ∠D = 75°. ∴ The measure of vertex ∠D is 75°.

If O is the circumcentre lying inside the ΔDEF with value of ∠EOF equal to 150°, find the measure of ∠D?1. 150° 2. 30° 3. 165° 4. 75°

Answer» Correct Answer - Option 4 : 75°

Given:

O is the circumcentre inside the ΔDEF.

∠EOF = 150°

Concepts used:

The measure of the angle formed with the given base at circumcentre = 2 × vertex angle formed opposite to the same base

Calculation:

⇒ ∠EOF = 2 × ∠D

⇒ 150° = 2 × ∠D

⇒ ∠D = 150°/2

⇒ ∠D = 75°.

∴ The measure of vertex ∠D is 75°.