Question

Four angles are formed by the intersection of the diagonals of this quadrilateral. Which statement is NOT true?

See attached image to see diagram & options.
(THERE'S TWO OF THE SAME IMAGE ACCIDENTALLY DID IT TWICE (:  )

Answer 1

m<1 = m < 2, that is what I think the answer is

Answer 2

4. The statement:
`m\angle 1=m\angle 2` is not true.

Explanation:

We have been given a graph of a quadrilateral and four angles formed by the intersection of the diagonals of this quadrilateral. We are asked to find the statement that is not true about our given angles.

Let us see our given choices one by one.

1.
`\angle 1\text{ and }\angle 2` are adjacent.

We can see that angle 1 and angle 2 are next to each other, therefore, 1st option is true.

2.
`m\angle 2=180^o-120^o`.

We can see from our given diagram that angle 2 and the angle with measure 180 degrees are linear pair of angles, so they will add up-to 180 degrees.

`m\angle 2+120^o=180^o`

Upon subtracting 120 degrees from both sides of our equation we will get,

`m\angle 2+120^o-120^o=180^o-120^o`

`m\angle 2=180^o-120^o`

Therefore, 2nd option is also true.

3.
`m\angle 1=120^o` because angle 1 and the 120 degree angle are vertical angles.

Since we know that vertical angles are equal, therefore, option 3rd option is true indeed.

4.
`m\angle 1=m\angle 2`

We can find measure of angle 2 by using the equation:

`m\angle 2=60^o`

Since measure of angle 1 is 120 degrees and measure of angle 2 is 60 degrees, therefore, 4th statement is not true.