Question

find the measure of ∠lnh.
(5x - 21)°
(3x + 17)°
a) what type of angle pair is shown?
alternate interior
alternate exterior
same side interior
same side exterior
corresponding
linear pair
vertical
b) are the angles congruent or supplementary?
congruent(∠1 = ∠2)
supplementary(∠1 + ∠2 = 180°)
c) solve for x.
check your work. keep trying.
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Explanation:

Step1: Identify angle - pair type

The angles $(5x - 21)^{\circ}$ and $(3x + 17)^{\circ}$ are alternate interior angles as they are between the two parallel - like lines and on opposite sides of the transversal.

Step2: Determine congruence or supplementarity

Alternate interior angles are congruent when the lines are parallel. So, we set up the equation $5x-21 = 3x + 17$.

Step3: Solve the equation for x

Subtract $3x$ from both sides:
$5x-3x-21=3x - 3x+17$
$2x-21 = 17$
Add 21 to both sides:
$2x-21 + 21=17 + 21$
$2x=38$
Divide both sides by 2:
$x=\frac{38}{2}=19$

Step4: Find the measure of $\angle LNH$

Substitute $x = 19$ into the expression for $\angle LNH=(3x + 17)^{\circ}$
$\angle LNH=3\times19 + 17=57+17 = 74^{\circ}$

Answer:

a) Alternate Interior
b) Congruent ($\angle1=\angle2$)
c) $x = 19$
$\angle LNH=74^{\circ}$