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DUBUTAETOGO DUBUTAETOGO

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UK2019GO UK2019GO · Answer 1

✏️CIRCLES

[tex]\red{••••••••••••••••••••••••••••••••••••••••••••••••••}[/tex]

[tex]\underline{\mathbb{ANSWERS:}}[/tex]

[tex] \qquad\Large\rm» \:\: 1. \: \green{m \angle A = 45 \degree} [/tex]

[tex] \qquad\Large\rm» \:\: 2. \: \green{m \angle A = 25 \degree} [/tex]

[tex] \qquad\Large\rm» \:\: 3. \: \green{m\overset{\frown}{BC} = 80\degree} [/tex]

[tex] \qquad\Large\rm» \:\: 4. \: \green{m\angle{BOC} = 110\degree} [/tex]

[tex] \qquad\Large\rm» \:\: 5. \: \green{m\angle{C} = 140\degree} [/tex]

[tex] \qquad\Large\rm» \:\: 6. \: \green{m\angle{C} = 35\degree} [/tex]

[tex] \qquad\Large\rm» \:\: 7. \: \green{m\angle{B} = 15\degree} [/tex]

[tex] \qquad\Large\rm» \:\: 8. \: \green{m\angle{B} = 60\degree} [/tex]

[tex] \qquad\Large\rm» \:\: 9. \: \green{m\angle{C} = 20\degree} [/tex]

[tex] \qquad\Large\rm» \:\: 10. \: \green{m\overset{\frown}{AC} = 120 \degree} [/tex]

[tex]\red{••••••••••••••••••••••••••••••••••••••••••••••••••}[/tex]

[tex]\underline{\mathbb{SOLUTIONS:}}[/tex]

#1. Find the measure of inscribed angle A that intercept the arc BC measuring 90°.

[tex] \rm m \angle A= \frac{1}{2}(90 \degree) \\ [/tex]

[tex] \rm m \angle A = 45 \degree[/tex]

[tex]\red{••••••••••••••••••••••••••••••••••••••••••••••••••}[/tex]

#2. Find the measure of inscribed angle A that intercept the arc BC measuring 50°.

[tex] \rm m \angle A= \frac{1}{2}(50\degree) \\ [/tex]

[tex] \rm m \angle A = 25\degree[/tex]

[tex]\red{••••••••••••••••••••••••••••••••••••••••••••••••••}[/tex]

#3. Find the measure of arc BC that is twice the measure of inscribed angle A.

[tex] \rm m\overset{\frown}{BC} = 2(40\degree) [/tex]

[tex] \rm m\overset{\frown}{BC} = 80\degree[/tex]

[tex]\red{••••••••••••••••••••••••••••••••••••••••••••••••••}[/tex]

#4. Solve for the measure of arc BC that is twice the measure of inscribed angle A.

[tex] \rm m\overset{\frown}{BC} = 2(55\degree) [/tex]

[tex] \rm m\overset{\frown}{BC} = 110\degree[/tex]

» The measure of the central angle BOC is as same as the measure of its intercepted arc BC.

[tex] \rm m\angle{BOC} = 110\degree[/tex]

[tex]\red{••••••••••••••••••••••••••••••••••••••••••••••••••}[/tex]

#5. The two opposite angles of a quadrilateral are supplementary.

[tex] \rm m\angle{C} + 40 \degree = 180\degree[/tex]

[tex] \rm m\angle{C} = 180\degree - 40 \degree[/tex]

[tex] \rm m\angle{C} = 140 \degree[/tex]

[tex]\red{••••••••••••••••••••••••••••••••••••••••••••••••••}[/tex]

#6. Find the measure of intercepted arc BC that is twice the measure of inscribed angle A.

[tex] \rm m\overset{\frown}{BC} = 2(55\degree) [/tex]

[tex] \rm m\overset{\frown}{BC} = 110\degree[/tex]

» Arc ABC is a semicircle, then arc AB and BC are supplementary.

[tex] \rm m\overset{\frown}{AB} + 110\degree = 180\degree [/tex]

[tex] \rm m\overset{\frown}{AB} = 180\degree - 110\degree[/tex]

[tex] \rm m\overset{\frown}{AB} = 70\degree[/tex]

» Find the measure of inscribed angle C that intercept the arc AB measuring 70°.

[tex] \rm m \angle C = \frac{1}{2} (70\degree) \\ [/tex]

[tex] \rm m \angle C = 35\degree[/tex]

[tex]\red{••••••••••••••••••••••••••••••••••••••••••••••••••}[/tex]

#7. Arc ACB is a semicircle, then arc AC and CB are supplementary.

[tex] \rm m\overset{\frown}{AC} + 150 \degree = 180\degree [/tex]

[tex] \rm m\overset{\frown}{AC} = 180\degree - 150 \degree[/tex]

[tex] \rm m\overset{\frown}{AC} = 30 \degree[/tex]

» Find the measure of inscribed angle B that intercept the arc measuring 30°.

[tex] \rm m \angle B = \frac{1}{2} (30\degree) \\ [/tex]

[tex] \rm m \angle B = 15\degree[/tex]

[tex]\red{••••••••••••••••••••••••••••••••••••••••••••••••••}[/tex]

#8. The two opposite angles of a quadrilateral are supplementary.

[tex] \rm m\angle{B} + 120\degree = 180\degree[/tex]

[tex] \rm m\angle{B} = 180\degree - 120\degree[/tex]

[tex] \rm m\angle{B} = 60\degree[/tex]

[tex]\red{••••••••••••••••••••••••••••••••••••••••••••••••••}[/tex]

#9. Find the measure of intercepted arc BC that is twice the measure of inscribed angle A.

[tex] \rm m\overset{\frown}{BC} = 2(70\degree) [/tex]

[tex] \rm m\overset{\frown}{BC} = 140 \degree[/tex]

» Arc ABC is a semicircle, then arc AB and BC are supplementary.

[tex] \rm m\overset{\frown}{AB} + 140\degree = 180\degree [/tex]

[tex] \rm m\overset{\frown}{AB} = 180\degree - 140\degree[/tex]

[tex] \rm m\overset{\frown}{AB} = 40\degree[/tex]

» Find the measure of inscribed angle C that intercept the arc AB measuring 40°.

[tex] \rm m \angle C = \frac{1}{2} (40\degree) \\ [/tex]

[tex] \rm m \angle C = 20\degree[/tex]

[tex]\red{••••••••••••••••••••••••••••••••••••••••••••••••••}[/tex]

#10. Find the measure of intercepted arc CB that is twice the measure of inscribed angle A.

[tex] \rm m\overset{\frown}{CB} = 2(30\degree) [/tex]

[tex] \rm m\overset{\frown}{CB} = 60\degree[/tex]

[tex]\red{••••••••••••••••••••••••••••••••••••••••••••••••••}[/tex]

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