Question

Two parallel lines are cut by a transversal and two of the same sides interior angle formed have measures of (4x+3)and(x+2)

Answer 1

Answer:

Therefore,

A. ∠BMN + ∠MND  = 180°

B . x = 35

C. $m\angle BMN = 143\°\\\\m\angle MND = 47\°$

Step-by-step explanation:

Given:

Consider  the Figure below such that

AB || CD

PQ as transversal

m∠BMN = (4x+3) and

m∠MND = (x+2)

To Find:

1. Relation between interior angles

2. x = ?

3. m∠BMN = ? and m∠MND = ?

Solution:

Same Side Interior Postulate:

The same-side interior angle theorem states that "when two lines that are parallel are intersected by a transversal line, the same-side interior angles that are formed are supplementary, or add up to 180 degrees".

As,  AB || CD

PQ as transversal

∠BMN and ∠MND  are Same Side Interior angles.

∴ ∠BMN + ∠MND  = 180° ......Relationship between the angles.

Substituting the values we get

$(4x+3)+(x+2)=180\\5x+5=180\\5x=175\\\\x=\dfrac{175}{5}=35$

Substitute 'x' in ∠BMN and ∠MND we get

$m\angle BMN = 4\times 35 +3=143\°\\\\m\angle MND = 45+2=47\°$

Therefore,

A. ∠BMN + ∠MND  = 180°

B . x = 35

C. $m\angle BMN = 143\°\\\\m\angle MND = 47\°$