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Direction: Find the following. 1. 2. 3. 5. Fund 21 Find m2A Find mBOX Find m2 Find BC O o 6. 7. 8. 9. 10. Find m2 Find m2B Find . Find m2 Find m2 AC​

Direction Find The Following 1 2 3 5 Fund 21 Find M2A Find MBOX Find M2 Find BC O O 6 7 8 9 10 Find M2 Find M2B Find Find M2 Find M2 AC class=

Sagot :

MasterOfMathProblemidn

✒️CIRCLES

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

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

  • [tex]\tt m \angle A = \red{45 \degree}[/tex]

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

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

  • [tex] \tt m \angle A =\red{ 25\degree}[/tex]

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

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

  • [tex] \tt m\overset{\frown}{BC} =\red{ 80\degree}[/tex]

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

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

  • [tex] \tt 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] \tt m\angle{BOC} = \red{110\degree}[/tex]

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

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

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

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

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

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

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

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

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

  • [tex] \tt m \angle C = \red{35\degree}[/tex]

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

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

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

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

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

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

  • [tex] \tt m \angle B = \red{15\degree}[/tex]

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

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

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

  • [tex] \tt m\angle{B} = \red{60\degree}[/tex]

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

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

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

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

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

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

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

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

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

  • [tex] \tt m \angle C = \red{20\degree}[/tex]

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