Anonymous
Anonymous asked in Education & ReferenceStandards & Testing · 6 years ago

SAT question?

How do we solve it?

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  • 6 years ago
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    The sum of the interior angles of any triangle will be 180°. Looking at ∆ACE, we see that we already have two angles. To find the third angle (∠AEC), we know that:

    3a + a + m∠AEC = 180

    ⇒ m∠AEC = 180 − 4a

    Since line CE intersects line AD, we also know that ∠AEC is a supplementary angle to ∠CED. So:

    m∠CED = 180 − m∠AEC

    = 180 − (180 − 4a)

    = 4a

    We also know that m∠DFE is opposite to the 60° angle, and they therefore have the same measure.

    Now that we have m∠CED (which will be the same as m∠FED) and m∠DFE, and we know that the sum of interior triangles is 180, we can find the missing value of a:

    m∠DFE + m∠FED + m∠DEF = 180

    ⇒ 60 + 4a + 2a = 180

    ⇒ 60 + 6a = 180

    ⇒ 6a = 120

    ⇒ a = 20°

    You can check your work by plugging a = 20 into the appropriate angles and seeing if they all add up to 180° as expected.

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