In ΔBCD, \overline{BD} BD is extended through point D to point E, \text{m}\angle BCD = (2x-1)^{\circ}m∠BCD=(2x−1) ∘

Question

In ΔBCD, \overline{BD}
BD
is extended through point D to point E, \text{m}\angle BCD = (2x-1)^{\circ}m∠BCD=(2x−1)
∘
, \text{m}\angle CDE = (7x-19)^{\circ}m∠CDE=(7x−19)
∘
, and \text{m}\angle DBC = (x+10)^{\circ}m∠DBC=(x+10)
∘
. Find \text{m}\angle CDE.m∠CDE.

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RuslanHeatt 3 years 2021-08-01T02:02:36+00:00 1 Answers 183 views 0

Answers ( )

  1. thienthanh
    0
    2021-08-01T02:04:11+00:00
    Reply

    Answer:

    30degrees

    Step-by-step explanation:

    Given

    Exterior angle m<CDE = 7x – 19 degrees

    interior angles are

    m<BCD = 2x – 1

    m<DBC = x+10

    Since the sum of the interior angles is equal to the exterior, hence;

    2x – 1 + x+10 = 7x – 19

    3x + 9 = 7x – 19

    3x – 7x = -19 – 9

    -4x = -28

    x = 28/4

    x = 7

    Get m<CDE

    m<CDE = 7x – 19

    m<CDE = 7(7) – 19

    m<CDE = 49 – 19

    m<CDE = 30degrees

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