Question

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

m∠P is greater than m∠O
m∠P is less than m∠O
m∠P = m∠O
m∠2 = m∠O

Answer 1

@DisplayError Can u help plz?

Answer 2

i think its m∠P is less than m∠O,am i right?

Answer 3

Why do you think angle P is less than angle O?

Answer 4

Not that it's wrong, but how would you reason through it?

Answer 5

im just guessing

Answer 6

am i right?

Answer 7

Oh, but do you have an idea? Not just a guess? Here's my reasoning (don't take it to be correct, but rather try to see if it makes sense):
Look at angle 2. Instead of it being labelled 2, set it equal to 2(O) (i.e. twice the measure of angle O). If this is true, then because angle 2 lies on the straight line HP, then angles 1 + 2 = 180 (supplementary angles). Using our substitution from before, angle 1 must then be 180 - 2(O). Again, remember that the sum of the angles in a triangle must equal 180, so
\[180 - 2(O) + O = 180 - O\]
For the sum of the angles to equal 180 (the expression above), angle P must equal angle O.

Answer 8

well that does make sense:)thx