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Pls help:))) geometry?

I have the answers but not sure how to get them. It doesn't make sense to me!

Bonus answer:

Angle 1, 3, 4, 6, and 9 = 20

Angle 2= 40

Angle 5 = 40

Angle 8 = 60

Angle 7= 140

Thanks and pls walk me into these steps!!!!

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  • 6 years ago
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    since △AEC is Isosceles, then m ∠ 3 = m ∠ 4.

    since △ADC is equilateral, m ∠ 3 + m ∠ 2 = m ∠ 4 + m ∠ 5 which means m ∠ 2 = m ∠ 5.

    therorefore, m ∠ 1 = m ∠ 6

    we have a fact that m ∠ 9 = m ∠ 1 = m ∠ 3 which we can say then:

    ∠ 9 = m ∠ 1 = m ∠ 3 = m ∠ 4 = m ∠ 6

    since △ADC is equilateral, the angles are all 60°. So, m ∠ 8 = 60° AND

    m ∠ 2 + m ∠ 3 = 60° & m ∠ 4 + m ∠ 5 = 60°.

    we know the fact that triangle angles add up to 180°. So,

    (m ∠ 1 + m ∠ 2 + m ∠ 3) + (m ∠ 4 + m ∠ 5 + m ∠ 6) + m ∠ 9 = 180° <---- substitute;

    (m ∠ 1 + 60°) + (60° + m ∠ 6) + m ∠ 9 = 180°

    m ∠ 1 + m ∠ 6 + m ∠ 9 = 180° - 120°

    m ∠ 1 + m ∠ 6 + m ∠ 9 = 60° since they are all the same, each is 20° So,

    ∠ 9 = m ∠ 1 = m ∠ 3 = m ∠ 4 = m ∠ 6 = 20°

    which means m ∠ 2 + m ∠ 3 = 60° as m ∠ 2 + 20° = 60° ----> m ∠ 2 = m ∠ 5 = 40°

    m ∠ 7 + m ∠ 3 + m ∠ 4 = 180°

    m ∠ 7 + 20° + 20° = 180°

    m ∠ 7 = 180° - 40°

    m ∠ 7 = 140°

    Hope it Helps :)

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