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5) If AABC ASDF and mA = 3x + 5, mzB = 5x-9 and mz5= 1.5x + 17. Find mzB.

A. mzB = 7°
8. m2B-8"
C. mzB 26°
D. mzB 31°

SHOW WORK!!!!!!!

User Bill Reiss
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1 Answer

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We can start by using the fact that AABC is an isosceles triangle to find the measure of angle AAB:

mAA + mAB + mAC = 180 (sum of angles in a triangle)

Since AABC is isosceles, we know that angle AAB is congruent to angle AAC:

mAA = mAC

Substituting this into the equation above, we get:

mAA + mAB + mAA = 180

2mAA + mAB = 180

Simplifying, we get:

mAB = 180 - 2mAA

Next, we can use the given angle measures to set up an equation involving angle ABZ:

mABZ = mAB - m5 - mZB

Substituting the given angle measures, we get:

mABZ = (180 - 2mAA) - (1.5x + 17) - (5x - 9)

Simplifying and collecting like terms, we get:

mABZ = 166 - 6.5x - 2mAA

We still need to find the measure of angle AAB, which we can do by using the equation for mA:

mA = 3x + 5

Since AABC is isosceles, we know that angle AAB is congruent to angle AAC, which means that mAAB = mAAC. Using the equation for mA, we can write:

mAAB = mAAC = 3x + 5

Now we can substitute this into the equation for mABZ:

mABZ = 166 - 6.5x - 2(mAAB)

Substituting mAAB, we get:

mABZ = 156 - 12.5x

Now we can solve for x by using the fact that mABZ + mZB + mzB + mz5 = 360 (since they form a quadrilateral). Substituting the expressions for mABZ, mZB, mzB, and mz5, we get:

156 - 12.5x + 5x - 9 + 1.5x + 17 = 360

Simplifying and solving for x, we get:

-5.5x = 196

x = -36

However, this value of x does not make sense since the measures of angles in a triangle and quadrilateral must be positive. Therefore, there is no solution that satisfies the given conditions and the answer is "no solution".
User Sebin Sunny
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