Find the measure of the missing angles. 100° b = C=

Mathematics

2 answers:

Rudiy273 years ago

8 0

Answer:

<b = 80

<c = 80

Step-by-step explanation:

<b and 100 form a straight line so they add to 180

<b +100 =180

<b = 180-100

<b = 80

angles b and c are vertical angles and vertical angles are equal

<c = <b = 80

konstantin123 [22]3 years ago

5 0

b+100 = 180° (straight line angles)

b= 180°- 100°

b= 80°

c= b (vertically opposite angles)

c= 80°

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SOLUTION:
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a + b = 10 (Equation 1)

"When the digits are reversed, the new number is 18 less than the original number" is algebraically written as
ba = ab - 18
>> bx10 + ax1 = (ax10 + bx1) - 18
>> 10b + a = 10a + b - 18
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>> 9(a - b) = 18
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>> a = b + 2 (Equation 2)

Now substitute equation 2 in equation 1 to get
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>> (b + 2) + b = 10
>> 2b = 8
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Plug this value back in equation 1 to get
a = b + 2 = 4 + 2 = 6

So a = 6 and b = 4. Hence, the original number is 64.

CHECK:
Given: The sum of the digits of a two-digit number is 10
Check: 6 + 4 = 10 (so it is true)

Given: When the digits are reversed, the new number is 18 less than the original number
Check:
Digits reversed: 64 reversed becomes new number 46, and 46 is 18 less than 64, that is, 46 = 64 - 18.

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