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27 September, 01:10

In quadrilateral ABCD, the measure of angle A is half the sum of the measures of the other angles. What is the measure of angle A? Express your answer to the nearest integer.

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  1. 27 September, 03:07
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    Angle A measures 120°.

    Step-by-step explanation:

    Step 1; Summing all the angles in a quadrilateral equals 360°. So the sum of angles A, B, C, and D will equal 360°. It is given that angle A is half the sum of angles B, C, D. Assume angle B = x, angle C = y, angle D = z.

    Angle A = x+y+z / 2, take this as equation 1.

    Step 2; Since ABCD is a quadrilateral,

    x+y+z = 360, take this as equation 2.

    Substituting equation 1 in 2, we get

    (x+y+z) / 2 + x+y+z = 360°,

    Multiply 2 on the LHS due to LCM

    (x+y+z) + 2 * (x+y+z) = 360°,

    [ (x+y+z) + 2 * (x+y+z) ]/2 = 360°.

    So we get a denominator of 2 on the LHS, so we multiply the entire equation by 2,

    3 * (x+y+z) = 360 * 2 = 720,

    (Angle B + Angle C + Angle D) = 720 / 3 = 240.

    So Angle B + Angle C + Angle D = 240,

    Angle A is half 240°, So angle A equals 240°/2 = 120°.
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