Stop 1: Philadelphia, PA
The Liberty Bell is one of the most famous sights in Philadelphia.
During its construction, the metal used was too brittle, causing it to
crack when it was first rung for a test strike. They recast it twice, but
it still ended up with the final crack in the bell that we can now see. No
one is exactly sure when the final crack in the bell happened, though
there are many stories claiming to be the origin.
While checking out this historical item, you notice that the crack seems
to create a linear pair. The measure of appears to be about
less than . Find the measure of each angle.

Ask by Carroll Carlson. in the United States

Jan 23,2025

Question

Stop 1: Philadelphia, PA
The Liberty Bell is one of the most famous sights in Philadelphia.
During its construction, the metal used was too brittle, causing it to
crack when it was first rung for a test strike. They recast it twice, but
it still ended up with the final crack in the bell that we can now see. No
one is exactly sure when the final crack in the bell happened, though
there are many stories claiming to be the origin.
While checking out this historical item, you notice that the crack seems
to create a linear pair. The measure of appears to be about
less than . Find the measure of each angle.

Ask by Carroll Carlson. in the United States

Jan 23,2025

UpStudy AI · Accepted Answer

Given that the crack in the Liberty Bell creates a linear pair, we know that the sum of the measures of the two angles in a linear pair is always $$180^\circ$$.

Let's denote the measure of angle 1 as $$x$$ and the measure of angle 2 as $$x + 25^\circ$$.

Since the angles form a linear pair, we can set up the equation:

$$x + (x + 25^\circ) = 180^\circ$$

Solving this equation will give us the measure of each angle.
Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$x+\left(x+25\right)=180$$
- step1: Simplify:
  $$2x+25=180$$
- step2: Move the constant to the right side:
  $$2x=180-25$$
- step3: Subtract the numbers:
  $$2x=155$$
- step4: Divide both sides:
  $$\frac{2x}{2}=\frac{155}{2}$$
- step5: Divide the numbers:
  $$x=\frac{155}{2}$$
The measure of angle 1 is $$77.5^\circ$$ and the measure of angle 2 is $$77.5^\circ + 25^\circ = 102.5^\circ$$.
Each angle measures $$77.5^\circ$$ and $$102.5^\circ$$.

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