Question

17. Classify Each Angle Pair then find the value of X

Answer 1

Given -

• If l || m, m∠1 = (13x + 24)°, and m∠2 = (5x-6)°,

To find -

• m∠2.

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 -

$\rightarrow\sf{(13x+24)^{ \circ}+(5x-6)^{ \circ}=180^{ \circ}}$

$\rightarrow\sf{13x+5x+24-6=180}$

$\rightarrow\sf{18x+18=180}$

$\rightarrow\sf{18x+18=180}$

$\rightarrow\sf{18(x+1)=180}$

$\rightarrow\sf{x+1=\frac{180}{18}}$

$\rightarrow\sf{x+1=10}$

$\rightarrow\sf{x=10-1}$

$\rightarrow\boxed{\bf{x=9}}$

m∠2 = (5x-6)° = {5(9) - 6}° = {45 - 6}°= 39°

Henceforth, m∠2 = 39°