SOLUTION:
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Number 19:
[tex]\: \: \: \sf{M + H + C + R + A = 540°}[/tex]
[tex]\: • \: \: \sf{110 + 3x + 10 + 120 + 90 + 4x = 540°}[/tex]
[tex] \: • \: \: \sf{330 + 7x = 540°}[/tex]
[tex] \: • \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf{7x = 540 - 330}[/tex]
[tex] \: • \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf{7x = 210°}[/tex]
[tex] \: • \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf{7x = \frac{210}{7} }[/tex]
[tex] \: • \: \: \boxed{\sf{x = 30°}}[/tex]
So, the answer:
[tex] \: • \: \: \sf{m \angle A = 4x = 4 \times 30 = \boxed{ \sf{120°}}}[/tex]
[tex] \: • \: \: \sf{m \angle H = 3x + 10 = 3 \times 30 + 10 = \boxed{ \sf{100°}}}[/tex]
Number 20:
[tex] \: \: \: \sf{130 + 2x + 4x - 20 + 110 + 100 = 540°}[/tex]
[tex] \: • \: \: \sf{320 + 6x = 540°}[/tex]
[tex] \: • \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf{6x = 540 - 320}[/tex]
[tex]\: • \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf{6x = 220°}[/tex]
[tex] \: • \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf{6x = \frac{220}{6}}[/tex]
[tex] \: • \: \: \boxed{\sf{x =36.67 }}[/tex]
So, the answer:
[tex] \: • \: \: \sf{m \angle L = 4x - 20 = 4 \times 36.67 - 20 = \boxed{ \sf{126.68°}}}[/tex]
[tex] \: • \: \: \sf{m \angle P = 2x = 2 \times 36.67 = \boxed{ \sf{73.34°}}}[/tex]
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ANSWER:
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Therefore the answer:
19. m∠A = 120°
[tex]\: \: \: \: \: \:[/tex]m∠H = 100°
20. m∠L = 126.68°
[tex]\: \: \: \: \: \: \:[/tex]m∠P = 73.34°
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