Math help! Topic: Measures of angles.?

Please answer the following questions correctly. I have a test tomorrow and I've finished these problems but i want to double check that i understand and know how to do them.

1) If AB and CD intersect at E, m<AEC = x+10, and m<DEB = 2x-30, find m<AEC

2)The measure of the complement of an angle is 20degrees less than the measure of the angle. Find the number of degrees in the angle.

3)The measure of each base angle of an isosceles triangle is 15degrees more than the measure of a vertex angle. Find the measure of each angle.

4) The measure of an angle is 3 times that of another angle, and the some of these measures is 120degrees. What are the measures of the angles?

Thank you!

2 Answers

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  • 1 decade ago
    Favorite Answer

    1)

    m<AEC = m<DEB (vertically opposite angles)

    => x + 10 = 2x - 30

    x = 40

    m<AEC = 40 + 10 = 50 degrees

    2)

    let the angle = x

    complement of x = 90 - x

    so 90 - x = x - 20

    2x = 110

    x = 55 degrees

    3)

    let the base angle = x

    vertex angle in isosceles triangle = 180 - 2x

    so x = 180 - 2x + 15

    3x = 195

    each base angle, x = 65 degrees

    vertex angle = 180 - 130 = 50 degrees

    4)

    let A and B are the angles

    A = 3B

    A + B = 120

    => 3B + B = 120

    4B = 120

    B = 30 and A = 90 degrees

  • 4 years ago

    a million. a+3a+5a=a hundred and eighty 9a=a hundred and eighty a=20 angle1=20, angle2=60, angle3=a hundred 2 a)2x+x+30+3x-30=a hundred and eighty 6x+30-30=a hundred and eighty 6x=a hundred and eighty x=30 ok=60, L=60, M=60 b) equilateral(or equivalent attitude uncertain what the be conscious is however) wish it enables

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