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Any thoughts how 1 could work alone? Thank you

This topic has 1 expert reply and 0 member replies
Ehab Salah Newbie | Next Rank: 10 Posts
Joined
17 Jan 2017
Posted:
2 messages

Any thoughts how 1 could work alone? Thank you

Post Sat Nov 04, 2017 5:51 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    ttps://postimg.org/image/1hvyms5n6j/" target="_blank">
    $$$$

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    Post Tue Nov 07, 2017 8:47 am
    Quote:


    In the figure shown, point O is the center of the semicircle and points B, C, and D lie on the semicircle. If the length of line segment AB is equal to the length of line sement OC, what is the degree measure of angle BAO?

    (1) The degree measure of angle COD is 60º
    (2) The degree measure of angle BCO is 40º
    Target question: What is the degree measure of ∠BAO?

    Given: The length of line segment AB is equal to the length of line sement OC

    Statement 1: The degree measure of angle COD is 60º
    So, we have the following:
    ttp://postimg.org/image/efttt9m8v/" target="_blank">

    Since the radii must have equal lengths, we can see that OB = OC
    ttp://postimg.org/image/yeea9dwbj/" target="_blank">

    So, ∆ABO is an isosceles triangle.
    ttp://postimg.org/image/qk93a8z4v/" target="_blank">

    If we let ∠BAO = x degrees, then we can use the facts that ∆ABO is isosceles and that angles must add to 180º to get the following:
    ttp://postimg.org/image/4p13h1d5r/" target="_blank">

    Since angles on a LINE must add to 180º, we know that ∠OBC = 2x
    ttp://postimg.org/image/3lgz52sin/" target="_blank">

    Now, we can use the facts that ∆BCO is isosceles and that the angles must add to 180º to get the following:
    ttp://postimg.org/image/oeesfqvof/" target="_blank">

    Finally, we can see that the 3 angles with blue circles around them are on a line.
    ttp://postimg.org/image/pzynlava7/" target="_blank">
    So, they must add to 180 degrees.
    We get: x + (180-4x) + 60 = 180
    Simplify: 240 - 3x = 180
    Solve to get: x = 20
    In other words, ∠BAO = 20º
    Since we can answer the target question with certainty, statement 1 is SUFFICIENT

    Statement 2: The degree measure of angle BCO is 40º
    So, we have the following:
    ttp://postimg.org/image/577btc8lv/" target="_blank">

    Since the radii must have equal lengths, we can see that OB = OC
    ttp://postimg.org/image/gktv4jj4j/" target="_blank">

    So, ∆BCO is an isosceles triangle, which means OBC is also 40º
    ttp://postimg.org/image/xb58tvhjn/" target="_blank">

    Since angles on a line must add to 180 degrees, ∠ABO = 140º
    ttp://postimg.org/image/5z9zsjcsz/" target="_blank">

    Finally, since ∆ABO is an isosceles triangle, the other two angles must each be 20º
    ttp://postimg.org/image/au3oqtb4j/" target="_blank">
    As we can see, ∠BAO = 20º
    Since we can answer the target question with certainty, statement 2 is SUFFICIENT

    Answer = D

    Cheers,
    Brent

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