Question

Find the measures of ∠N and ∠P. PLEASE HELP!!!

Answer 1

Answer: choice A) both angles (N and P) are 25 degrees

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MN and MP are the same length as shown by the tickmarks (they are congruent segments). So angle N and angle P are the same measure

Angle N is 4b-19 while angle P is 2b+3. Set the two expressions equal to each other and solve for b

4b - 19 = 2b + 3

4b - 2b = 3+19

2b = 22

b = 22/2

b = 11

If b = 11, then,

angle N = 4*b - 19 = 4*11 - 19 = 44 - 19 = 25 degrees

angle P = 2*b + 3 = 2*11 + 3 = 22 + 3 = 25 degrees

As expected, angle N and angle P are the same measure

Note: this is an isosceles triangle because it has two sides that are the same length.

Answer 2

Both ∠N and ∠P measure to 25°

Explanation:

Given that we have an isosceles triangle, we know that angles N and P must be equivalent.

Therefore we can equate both expressions for angles N and P to solve for b

4b - 19 = 2b + 3 add 19 to both sides

4b = 2b + 22 take away 2b from both sides

2b = 22 divide both sides by 2 to isolate b

b = 11°

Check answers by plugging in 11° for b

∠N = 4(11°) - 19°

∠N = 44° - 19°

∠N = 25°

∠P = 2(11°) + 3°

∠P = 22° + 3°

∠P = 25°

Both angles measure to 25°