Question

calculate the value of x, then find the measure of the angle labeled a.
25)
26)
27)
28)
29)
30)

Explanation:

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25)

Step1: Sum angles to 180°

$$(x+48) + (x+71) + 71 = 180$$

Step2: Simplify and solve for x

$$2x + 190 = 180 \implies 2x = -10 \implies x = -5$$

Step3: Calculate angle A

$$x+48 = -5 + 48 = 43$$

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26)

Step1: Sum angles to 180°

$$(5x+6) + 77 + (3x+9) = 180$$

Step2: Simplify and solve for x

$$8x + 92 = 180 \implies 8x = 88 \implies x = 11$$

Step3: Calculate angle A

$$3x+9 = 3(11)+9 = 42$$

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27)

Step1: Sum angles to 90° (right triangle)

$$(x+19) + (5+5x) = 90$$

Step2: Simplify and solve for x

$$6x + 24 = 90 \implies 6x = 66 \implies x = 11$$

Step3: Calculate angle A

$$x+19 = 11 + 19 = 30$$

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28)

Step1: Sum angles to 180°

$$(6x-4) + (8x+8) + 50 = 180$$

Step2: Simplify and solve for x

$$14x + 54 = 180 \implies 14x = 126 \implies x = 9$$

Step3: Calculate angle A

$$6x-4 = 6(9)-4 = 50$$

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29)

Step1: Sum angles to 180°

$$70 + (7x-1) + (6x+7) = 180$$

Step2: Simplify and solve for x

$$13x + 76 = 180 \implies 13x = 104 \implies x = 8$$

Step3: Calculate angle A

$$7x-1 = 7(8)-1 = 55$$

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30)

Step1: Sum angles to 180°

$$(8+6x) + (5x+5) + 79 = 180$$

Step2: Simplify and solve for x

$$11x + 92 = 180 \implies 11x = 88 \implies x = 8$$

Step3: Calculate angle A

$$8+6x = 8+6(8) = 56$$

Answer:

1. $x=-5$, Angle A = $43^\circ$
2. $x=11$, Angle A = $42^\circ$
3. $x=11$, Angle A = $30^\circ$
4. $x=9$, Angle A = $50^\circ$
5. $x=8$, Angle A = $55^\circ$
6. $x=8$, Angle A = $56^\circ$