Pa Help Dito Math 10 (Serious Answers Please) 1. M∠ACB A.63 B.31.5 C.140…

Pa help dito Math 10 (Serious Answers please)

1. m∠ACB

A.63

B.31.5

C.140

D.70

2. m∠ADB

A.63

B.31.5

C.140

D.70

3.m arc ADE

A.38

B.180

C.63

D.117

4. m arc DE

A.38

B.180

C.63

D.117

5.m arc BE

A.38

B.180

C.63

D.117

✒️CIRCLES

[tex]••••••••••••••••••••••••••••••••••••••••••••••••••[/tex]

[tex] \large\underline{\mathbb{PROBLEM}:} [/tex]

  • In the figure, AE is a diameter, the measure of arc AD is 142 and the measure of arc AB is 63. Find the indicated measures.

[tex]••••••••••••••••••••••••••••••••••••••••••••••••••[/tex]

[tex] \large\underline{\mathbb{ANSWER}:} [/tex]

[tex] \qquad \Large 1) \: \rm{A. \: 63} [/tex]

[tex] \qquad \Large 2) \: \rm{B. \: 31.5} [/tex]

[tex] \qquad \Large 3) \: \rm{B. \: 180} [/tex]

[tex] \qquad \Large 4) \: \rm{A. \: 38} [/tex]

[tex] \qquad \Large 5) \: \rm{D. \: 117} [/tex]

[tex]••••••••••••••••••••••••••••••••••••••••••••••••••[/tex]

[tex] \large\underline{\mathbb{SOLUTION}:} [/tex]

#1: Find m∠ACB

  • The measure of central angle ACB is as same as the measure of its intercepted arc AB. Therefore, the measure of angle ACB is also 63°

#2: Find m∠ADB

  • The measure of inscribed angle ADB is half the measure of its intercepted arc AB. Therefore, half of 63° is 31.5° that is the measure of angle ADB.

#3: Find m(arc)ADE

  • Arc ADE is a semicircle arc since AE is a diameter. Therefore, its measure is 180°, same as arc ABE.

#4: m(arc)DE

  • The sum of the measures of arcs AD and DE is 180° since arc ADE is a semicircle arc. Arc ADE minus arc AD is arc DE (180 – 142 = 38). Therefore, the measure of arc DE is 38°.

#5: m(arc)BE

  • The sum of the measures of arcs AB and BE is 180° since arc ABE is a semicircle arc. Arc ABE minus arc AB is arc BE (180 – 63 = 117). Therefore, the measure of arc BE is 117°.
See also  Part III. Problem Solving (4 Points Per Item) Solve The Following Proble...

[tex]••••••••••••••••••••••••••••••••••••••••••••••••••[/tex]

(ノ^_^)ノ