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5 days ago

If mBC = (9x-53) and mCD = (2x + 45) find mBAD

Mathematics

1 answer:

babunello [3.6K]5 days ago

7 0

Answer:

$m\angle BAD=73^o$

Step-by-step explanation:

The diagram related to the question is in the attached figure.

Step 1

Determine the value of x

Let:

O ----> denote the center of the circle

It is known that:

Triangle BOC is congruent to Triangle COD

$m\angle BOC=arc\ BC$ ----> due to the central angle

$m\angle COD=arc\ CD$ ----> according to the central angle

$m\angle BOC=m\angle COD$

Thus:

$arc\ BC=arc\ CD$

Insert the provided values

$(9x-53)^o=(2x+45)^o$

Solve for x

$9x-2x=45+53\\7x=98\\x=14$

Step 2

Calculate the measure of angle BAD

It is known that:

The inscribed angle measures half that of the arc it subtends.

Thus:

$m\angle BAD=\frac{1}{2} [arc\ BC+arc\ CD]$

$arc\ BC=9(14)-53=73^o$

$arc\ CD=2(14)+45=73^o$

Insert values

$m\angle BAD=\frac{1}{2} [73^o+73^o]=73^o$

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If m<9=97° and m<12=114°, find each measure. I have to show my work.

Leona [4166]

Solution/Step-by-step breakdown:

Information provided:

m<9 = 97°

m<12 = 114°

a. m<1 = m<9 because they are corresponding angles, which are equal.

m<1 = 97° (using substitution)

b. m<2 + m<1 = 180° (since they form a linear pair)

m<2 + 97° = 180° (substitute the value)

m<2 = 180 - 97 (subtracting 97 from both sides)

m<2 = 83°

c. m<3 = m<11 (as they are corresponding angles)

m<11 + m<12 = 180° (linear pair)

m<11 + 114° = 180° (substituting the known angle)

m<11 = 180 - 114

m<11 = 66°

m<3 = m<11 = 66°

d. m<4 + m<3 = 180° (linear pair)

m<4 + 66° = 180° (substituting the known angle)

m<4 = 180 - 66

m<4 = 114°

e. m<5 = m<2 as vertical angles are equal.

m<5 = 83° (using substitution)

f. m<6 = m<1 (vertical angles are equal)

m<6 = 97° (using substitution)

g. m<7 = m<4 (as vertical angles are equal)

m<7 = 114° (using substitution)

h. m<8 = m<3 (due to vertical angles being equal)

m<8 = 66° (using substitution)

i. m<10 = m<2 (corresponding angles are equal)

m<10 = 83° (using substitution)

j. m<11 = m<3 (because they are vertical angles)

m<11 = 66° (using substitution)

k. m<13 = m<5 (corresponding angles)

m<13 = 83° (applying substitution)

l. m<14 = m<9 (as vertical angles)

m<14 = 97° (applying substitution)

m. m<15 = m<12 (as vertical angles)

m<15 = 114° (applying substitution)

n. m<16 = m<11 (because they are vertical angles)

m<16 = 66° (applying substitution)

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