Question

Which of the following statements must be true about this diagram? Check all that apply.

A. m<3 is greater than m<2
B. m<4 is greater than m<1
C. m<4 is greater than m<2
D. The degree measure of <3 equals the sum of the degree measures of <1 and <2.
E. The degree measure of <4 equals the sum of the degree measures of <1 and <2.
F. the degree measure of <4 equals the sum of the degree measures of <2 and <3.

Answer 1

Option B, C and E are the correct options.

Explanation:

By exterior angle theorem sum of two opposite interior angles is equal to the exterior angle of a triangle.

By this theorem we can easily say

∠4 = ∠1 + ∠2

Where ∠4 is exterior angle and ∠1, ∠2 are opposite interior angles of the triangle.

Now we know sum of angle 1 and 2 is equal to angle 4 which shows ∠4 is greater than ∠1 and ∠2 both.

Therefore options B, C, E are the correct options.

Answer 2

Answer: options B, C, E will be correct according to the given diagram.

Explanation:

Since, according to the Exterior Angle theorem, In a triangle the sum of any two adjacent interior angles is equal to the exterior angle of the triangle.

And, here
`\angle 4` is the exterior angle of the triangle, while
`\angle 1`,
`\angle 2`, and
`\angle 3` are the interior angles of the triangle.

Thus, according to the theorem,

`\angle 1+ \angle2=\angle 4`.

⇒
`\angle4 > \angle1`

and
`\angle4 > \angle2`

Therefore, options B, C, E are correct.