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
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[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.
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[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]
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[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°.
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