Question

1.
2.
3.
4.
5.
6.
7.
8.

Explanation:

Step1: Suma ángulos triángulo = 180°

$40^\circ + 100^\circ + (2x)^\circ = 180^\circ$

Step2: Resuelve para x

$140 + 2x = 180 \implies 2x = 40 \implies x=20$
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Step1: Suma ángulos triángulo = 180°

$35^\circ + 50^\circ + (x-10)^\circ = 180^\circ$

Step2: Resuelve para x

$85 + x -10 = 180 \implies x +75=180 \implies x=105$
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Step1: Suma ángulos triángulo = 180°

$(-12+9x)^\circ + 60^\circ + 60^\circ = 180^\circ$

Step2: Resuelve para x

$-12 +9x +120 = 180 \implies 9x +108=180 \implies 9x=72 \implies x=8$
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Step1: Suma ángulos triángulo = 180°

$46^\circ + 46^\circ + (2-3x)^\circ = 180^\circ$

Step2: Resuelve para x

$92 +2 -3x = 180 \implies 94 -3x=180 \implies -3x=86 \implies x=-\frac{86}{3}\approx-28.67$
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Step1: Suma ángulos triángulo = 180°

$71^\circ + 50^\circ + (6x-1)^\circ = 180^\circ$

Step2: Resuelve para x

$121 +6x -1 = 180 \implies 6x +120=180 \implies 6x=60 \implies x=10$
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Step1: Suma ángulos triángulo = 180°

$45^\circ + 90^\circ + (8x+2)^\circ = 180^\circ$

Step2: Resuelve para x

$135 +8x +2 = 180 \implies 8x +137=180 \implies 8x=43 \implies x=\frac{43}{8}=5.375$
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Step1: Suma ángulos triángulo = 180°

$(14x+27)^\circ + 64^\circ + 85^\circ = 180^\circ$

Step2: Resuelve para x

$14x +27 +149 = 180 \implies 14x +176=180 \implies 14x=4 \implies x=\frac{2}{7}\approx0.29$
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Step1: Suma ángulos triángulo = 180°

$44^\circ + 104^\circ + (18+7x)^\circ = 180^\circ$

Step2: Resuelve para x

$148 +18 +7x = 180 \implies 7x +166=180 \implies 7x=14 \implies x=2$

Answer:

1. $x=20$
2. $x=105$
3. $x=8$
4. $x=-\frac{86}{3}\approx-28.67$
5. $x=10$
6. $x=\frac{43}{8}=5.375$
7. $x=\frac{2}{7}\approx0.29$
8. $x=2$