Answer :
Answer:
Therefore,
A. ∠BMN + ∠MND = 180°
B . x = 35
C. [tex]m\angle BMN = 143\°\\\\m\angle MND = 47\°[/tex]
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
[tex](4x+3)+(x+2)=180\\5x+5=180\\5x=175\\\\x=\dfrac{175}{5}=35[/tex]
Substitute 'x' in ∠BMN and ∠MND we get
[tex]m\angle BMN = 4\times 35 +3=143\°\\\\m\angle MND = 45+2=47\°[/tex]
Therefore,
A. ∠BMN + ∠MND = 180°
B . x = 35
C. [tex]m\angle BMN = 143\°\\\\m\angle MND = 47\°[/tex]
