Question

If the measure of angle 2 is twice the measure of angle O, then which of the following must be true?

A. m∠P is greater than m∠O
B. m∠P is less than m∠O
C. m∠P = m∠O
D. m∠2 = m∠O

Answer 1

measure of angle 2 is twice the measure of angle O
so m<O = m<P

answer
C. m∠P = m∠O

Answer 2

Answer:-C. is the correct option."m∠P = m∠O"

Explanation:-

Let the measure of ∠O be x

Then ∠2= 2x ..........>Exterior angle of triangle

We know that for a triangle ,

Exterior angle= Sum of opposite interior angles

⇒∠2=∠O+∠P

⇒2x=x+∠P  [Substitute values of ∠O and ∠2]

⇒x=∠P   [Subtract x on both sides]

⇒∠P=∠O=x [Transitive property]

∴ C. is the correct option.