Which Statement Regarding the Diagram is True

The true statements are:

m∠ 3 + m∠ 4 = 180° ⇒ 1st

m∠ 2 + m∠ 4 + m∠ 6 = 180° ⇒ 2nd

m∠ 2 + m∠ 4 = m∠ 5 ⇒ 3rd

Step-by-step explanation:

* Look to the attached diagram to answer the question

# m∠ 3 + m∠ 4 = 180°

∵ ∠ 3 and ∠ 4 formed a straight angle

∵ The measure of the straight angle is 180°

∴ m∠ 3 + m∠ 4 = 180° ⇒ true

# m∠ 2 + m∠ 4 + m∠ 6 = 180°

∵ ∠ 2 , ∠ 4 , ∠ 6 are the interior angles of the triangle

∵ The sum of the measures of interior angles of any Δ is 180°

∴ m∠ 2 + m∠ 4 + m∠ 6 = 180° ⇒ true

# m∠ 2 + m∠ 4 = m∠ 5

∵ In any Δ, the measure of the exterior angle at one vertex of the

triangle equals the sum of the measures of the opposite interior

angles of this vertex

∵ ∠ 5 is the exterior angle of the vertex of ∠ 6

∵ ∠2 and ∠ 4 are the opposite interior angles to ∠ 6

∴ m∠ 2 + m∠ 4 = m∠ 5 ⇒ true

# m∠1 + m∠2 = 90°

∵ ∠ 1 and ∠ 2 formed a straight angle

∵ The measure of the straight angle is 180°

∴ m∠1 + m∠2 = 90° ⇒ Not true

# m∠4 + m∠6 = m∠2

∵ ∠ 4 , ∠ 6 , ∠ 2 are the interior angles of a triangle

∵ There is no given about their measures

∴ We can not says that the sum of the measures of ∠ 4 and ∠ 6 is

equal to the measure of ∠ 2

∴ m∠4 + m∠6 = m∠2 ⇒ Not true

# m∠2 + m∠6 = m∠5

∵ ∠ 5 is the exterior angle at the vertex of ∠ 6

∴ m∠ 2 + m∠ 6 = m∠ 5 ⇒ Not true

Let’s verify each case to determine the solution to the problem.

Statements

case A) m∠3 + m∠4 =

The statement is True

Because

Angle 3 and Angle 4 are supplementary angles

case B) m∠2 + m∠4 + m∠6 =

The statement is True

Because

The sum of the internal angles of a triangle is always equal to

case C) m∠2 + m∠4 = m∠5

The statement is True

Because

we know that

m∠2 + m∠4 + m∠6 =

—–> equation A (see case B)

m∠5 + m∠6 =

——-> by supplementary angles

m∠6 =
-m∠5 ——-> equation B

substitute equation B in equation A

m∠2 + m∠4 +
-m∠5 =

m∠2 + m∠4 = m∠5 ———> is ok

case D) m∠1 + m∠2=

The statement is False

Because

m∠1 + m∠2=

——-> by supplementary angles

case E) m∠4 + m∠6=m∠2

The statement is False

Because

we know that

m∠2 + m∠4 + m∠6 =

m∠4 + m∠6 =
-m∠2

m∠4 + m∠6=m∠2

-m∠2= m∠2

=2m∠2

m∠2=

the statement only will be true when the triangle be right triangle and

m∠2=

case F) m∠2 + m∠6 = m∠5

The statement is False

Because

we know that

m∠5 + m∠6 =

——-> by supplementary angles

m∠5=
-m∠6 —–> equation A

m∠2 + m∠6 = m∠5 ——–> equation B (given equation)

substitute equation A in equation B

m∠2 + m∠6 =-m∠6

m∠2 + 2m∠6 =

the statement only will be true when the triangle be isosceles and

m∠4=m∠6

therefore

the answer is

m∠3 + m∠4 =

m∠2 + m∠4 + m∠6 =

m∠2 + m∠4 = m∠5

m∠5 + m∠3 = m∠1   is true.

m∠5 + m∠6 = 180 is true

m∠2 +m∠3 = m∠6   is true

m∠2 +m∠3 +m∠5 = 180   is true

A,B,C. OR 1,2,3

Step-by-step explanation: