15.02.2023

Given: Lines y and z are parallel, and ABC
forms a triangle. Prove: m <5 + m<2 + m<6
180° Statements Reasons 1. ABC is a triangle
1. given 2. y I z 2. given 3. <1 = 45; <3 = <6
3.? 4. m<1= m<5; m<3 = m<6 4. def. = 5.
m<1+ m<2 + m<3 = m postulate 6. m<1 + m<2 + m<3 = 180° 6. def.
straight angle 7. m<5 + m<2 + m<6 = 180° 7.
substitution Which could be the missing
reason in Step 3? alternate interior angles
are congruent alternate exterior angles are
congruent vertical angles are congruent
corresponding angles are congruent

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Faq

Mathematics

Given: Lines y and z are parallel, and ABC forms a triangle. Prove: m∠5 + m∠2 + m∠6 = 180° Lines y and z are parallel. Triangle A B C sits between the 2 lines with point A on line y and points C and B on line z. Angle C A B is 2. Its exterior angle to the left is 1 and its exterior angle to the right is 3. Angle A B C is 6 and its exterior angle to the right is 7. Angle B C A is 5 and its exterior angle to the left is 4. Statements Reasons 1. ABC is a triangle 1. given 2. y ∥ z 2. given 3. ∠1 ≅ ∠5; ∠3 ≅ ∠6 3. ? 4. m∠1 = m∠5; m∠3 = m∠6 4. def. ≅

Step-by-step answer

P Answered by PhD

The correct option is;

Alternate interior angles

Step-by-step explanation:

The m∠5 + m∠2 + m∠6 = 180° proof is given as follows;

Statement Reason

1. ABC is a triangle Given

2. y ║ z Given

3. ∠1 ≅ ∠5; ∠3 ≅ ∠6 Alternate interior angles

4. m∠1 = m∠5; m∠3 = m∠6 Definition of (congruency) ≅

5. m∠1 + m∠2 + ∠3 = m∠LAM ∠Addition postulate

6. m∠1 + m∠2 + ∠3 = 180° Definition of straight angles

7. m∠5 + m∠2 + ∠6 = 180° Substitution property

Step 3;

Given that line y is parallel to line z, we have that the transversal AB will make equal corresponding angles with the lines y and z, therefore, ∠6 will be equivalent to segment AB extended

Which gives, ∠6 is supplementary to ∠a where ∠a = ∠1 + ∠2

Therefore, given that ∠3 is also supplementary to ∠a where as we have above, ∠a = ∠1 + ∠2, we have that ∠3 = ∠6 and ∠3 ≅ ∠6 where ∠3 and ∠6 are alternate interior angles;

Similarly, ∠1 ≅ ∠5 by alternate interior angles of two parallel lines property.

Given: Lines y and z are parallel, and ABC forms a triangle. Prove: m∠5 + m∠2 + m∠6 = 180° Lines y a

Mathematics

Given: lines y and z are parallel, and abc forms a triangle. prove: m∠5 + m∠2 + m∠6 = 180° statements reasons 1. abc is a triangle 1. given 2. y ∥ z 2. given 3. ∠1 ≅ ∠5; ∠3 ≅ ∠6 3. ? 4. m∠1 = m∠5; m∠3 = m∠6 4. def. ≅ 5. m∠1 + m∠2 + m∠3 = m∠lam 5. ∠ addition postulate 6. m∠1 + m∠2 + m∠3 = 180° 6. def. straight angle 7. m∠5 + m∠2 + m∠6 = 180° 7. substitution which could be the missing reason in step 3?

Step-by-step answer

P Answered by Specialist

126

alternate interior angles are congruent

Mathematics

Step-by-step answer

P Answered by PhD

Step-by-step explanation:

8. Statement

m<5+m<2+m<6=180

Reason

Substitution

Given: lines y and z are parallel, and abc forms a triangle. prove: m∠5 + m∠2 + m∠6 = 180° stateme

Mathematics

Given: Lines y and z are parallel, and ABC forms a triangle. Prove: m25 + m_2 + m26 = 180° M

Step-by-step answer

P Answered by Master

Brainliess pl

The answer in this question is Alternate interior angles are congruent.

Step-by-step explanation:

Alternate interior angles are defined as when the two lines are crossed by another line which is called transversal, the pairs of angles on opposite sides of the transversal but inside the two lines are known as alternate interior angles.

Mathematics

Given: Lines y and z are parallel, and ABC forms a triangle. Prove: m25+ m22 + m26 = 180° which could be the missing reason in step 3

Step-by-step answer

P Answered by Specialist

Explanation:

This problem has missing information, so I've provided my own diagram below.

By Alternate Interior Angles:

$m\angle 2=34^{\circ}$

Angles ∠6 and 48 degrees are supplementary:

$m\angle 6 + 48^{\circ}=180^{\circ} \\ \\ m\angle 6 =180^{\circ}- 48^{\circ} \\ \\ m\angle 6 =132^{\circ}$

Internal angles of every triangle add up to 180 degrees:

$m\angle 5+ m\angle 2 + m\angle 6 = 180^{\circ} \\ \\ m\angle 5+ 34^{\circ} + 48^{\circ} = 180^{\circ} \\ \\ m\angle 5= 180^{\circ}-34^{\circ}- 48^{\circ} \\ \\ m\angle 5=98^{\circ}$