please help asap!!! 1. ABCD is an isosceles trapezoid. m < A = 6x + 12 and m < d = 2x + 20. Angles B&C are congru

Question

please help asap!!!

1. ABCD is an isosceles trapezoid. m < A = 6x + 12 and m < d = 2x + 20. Angles B&C are congruent. What is the measure of angles B&C?

2. QRST is a rectangle. RS = 12k +5 and QT = 145. what is the value of ‘k’?

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Thanh Thu 4 years 2021-08-22T16:43:23+00:00 2 Answers 6 views 0

Answers ( )

  1. lethu
    0
    2021-08-22T16:44:33+00:00
    Reply

    Answer:

    Step-by-step explanation:

    #1). It could be good to provide us with the picture, because the answer depends from the angle we choose for letter A.

    — If angle A is acute, then m∠A = m∠D

    and

    6x + 12 = 2x + 20 ⇒ x = 2

    m∠A = m∠D = 24°

    m∠B = m∠C = 180° – 24° = 156°

    — If angle A is obtuse, then m∠A + m∠D = 180°

    and

    6x + 12 + 2x + 20 = 180 ⇒ x = 18.5

    m∠A = m∠B = 6(18.5) + 12 = 123°

    m∠D = m∠C = 2(18.5) + 20 = 57°

    #2). 12k + 5 = 145

    12k = 140

    k = \frac{35}{3} = 11\frac{2}{3}

  2. MichaelMet
    0
    2021-08-22T16:44:59+00:00
    Reply

    Answer:

    ∠ B = 123°, ∠ D = 57°

    Step-by-step explanation:

    Each lower base angle is supplementary to the upper base angle on the same side.

    ∠ A and ∠ D are on the same side, then

    6x + 12 + 2x + 20 = 180

    8x + 32 = 180 ( subtract 32 from both sides )

    8x = 148 ( divide both sides by 8 )

    x = 18.5

    Thus

    ∠ A = 6x + 12 = 6(18.5) + 12 = 111 + 12 = 123°

    ∠ D = 2x + 20 = 2(18.5) + 20 = 37 + 20 = 57°

    The lower base angles and the upper base angles are congruent, so

    ∠ B = ∠ A = 123°

    ∠ C = ∠ D = 57°

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