Given -
- If l || m, m∠1 = (13x + 24)°, and m∠2 = (5x-6)°,
To find -
Concept -
Whenever two parallel lines are cut by a transversal, an interesting relationship exists between the two interior angles on the same side of the transversal. These two interior angles are supplementary angles. Hence, according to the figure l and m are two parallel lines and t is the transversal intersecting them then ∠1 + ∠2 = 180°.
Solution -
[tex]\rightarrow\sf{(13x+24)^{ \circ}+(5x-6)^{ \circ}=180^{ \circ}}[/tex]
[tex]\rightarrow\sf{13x+5x+24-6=180}[/tex]
[tex]\rightarrow\sf{18x+18=180}[/tex]
[tex]\rightarrow\sf{18x+18=180}[/tex]
[tex]\rightarrow\sf{18(x+1)=180}[/tex]
[tex]\rightarrow\sf{x+1=\frac{180}{18}}[/tex]
[tex]\rightarrow\sf{x+1=10}[/tex]
[tex]\rightarrow\sf{x=10-1}[/tex]
[tex]\rightarrow\boxed{\bf{x=9}}[/tex]
m∠2 = (5x-6)° = {5(9) - 6}° = {45 - 6}°= 39°
Henceforth, m∠2 = 39°
