Question

Which statements are always true regarding the
diagram? Check all that apply.
3
OmZ3+ m 24 = 180°
A
co
On
m2 + m 24+ m26 = 180°
m2 + m 24 = m 25
2
7
m21+ m2 = 90°
m24+ m26 = m22
m22 + m 26 = m25

Answer 1

Answer:

m<3 + m<4:= 180°

m<2 + m<4 + m<6 = 180°

m<2 + m<4 = m<5

Step-by-step explanation:

<3 and <4 are linear pairs. They are angles on a straight line. Angles in a straight line sum up to give 180°. Therefore, the statement "m<3 + m<4:= 180°" is TRUE.

<2, <4, <6 are interior angles of a triangle. The sum of the angles in a ∆ = 180°. Therefore, the statement, "m<2 + m<4 + m<6 = 180°" is TRUE.

<2 and <4 are opposite interior angles of the ∆, while <5 is an exterior angle to the ∆. Based on the external angle theorem of a ∆, the statement, "m<2 + m<4 = m<5" is TRUE.

<1 and <2 are a linear pair, and are angles on a straight line. Their sum cannot give us 90°.

m<4 + m<6 ≠ m<2. Rather, 180 - (m<4 + m<6) = m<2 (sum of angles in a ∆)

m<2 + m<6 ≠ m<5. Rather, m<2 + m<4 = m<5

Answer 2

The correct equations are:

m∠5 + m∠6 = 180°

m∠2 + m∠3 =  m∠6

m∠2 + m∠3 + m∠5 = 180°

m∠2 + m∠5 =  m∠4

Triangle

Triangle is a polygon with three angles and three sides. The sum of angles in a triangle is 180 degree.

From the diagram:

m∠5 + m∠6 = 180° (angle in a straight line)

But:

m∠2 + m∠3 + m∠5 = 180

m∠2 + m∠3 + m∠5 = m∠5 + m∠6

m∠2 + m∠3 =  m∠6

Also:

m∠2 + m∠3 + m∠5 = 180° (sum of angles in a triangle)

But:

m∠3 + m∠4 = 180° (angle in a straight line)  

m∠2 + m∠3 + m∠5 = m∠3 + m∠4

m∠2 + m∠5 =  m∠4

Find out more on triangles at: https://brainly.com/question/2644832