C = 6.5x + 70 A caterer used the equation above to determine the total cost of a party, C. She charges a fixed fee, plus an additional fee of $6.50 per person, for x people. What is the fixed fee the caterer charges for the party

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153536

03.02.2022

Mathematics

1. x=56^o

2. Exterior angle = 116^o

Step-by-step explanation:

We can see from our given diagram that (2x+4) degrees is the measure of exterior angle of triangle PQR.

Since the measure of exterior angle of a triangle equals to the sum of the opposite interior angles. So measure of our given triangle's exterior angle will be equal to sum of measure of angle P and angle Q.

We can represent this information as:

(2x+4)^o=60^o+x^o

2x^o+4^o=60^o+x^o

Let us subtract x^o from both sides of our equation.

2x^o+4^o-x^o=60^o+x^o-x^o

x^o+4^o=60^o

Let us subtract 4^o from both sides of our equation.

x^o+4^o-4^o=60^o-4^o

x=56^o

Therefore, value of x is 56 degrees.

2. Since the measure of exterior angle of our given triangle is 2x+4, let us substitute x=56 in our expression to find the measure of exterior angle.

$\text{Measure of exterior angle}=(2x+4)^o$

$\text{Measure of exterior angle}=(2*56+4)^o$

$\text{Measure of exterior angle}=(112+4)^o$

$\text{Measure of exterior angle}=116^o$

Therefore, the measure of exterior angle of our given triangle is 116 degrees.

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