Question

Consider the quadrilateral ABCD below. What is the measure of ∠DAB of the

quadrilateral ABCD?


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Answer 1

Answer:

Measure of ∠DAB is  83°

Step-by-step explanation:

In Triangle ACD

    ∠ACD + ∠CDA + ∠DAC = 180°    ( sum of all angle of triangle is 180° )

⇒ 2k - 5 + 3k + 1 + 3k = 180°

⇒ 8k -4 = 180°

⇒ 8k = 184°

    ∴ k = 23°

In Triangle ABC

   ∠BAC + ∠ACB + ∠ABC = 180°      ( sum of all angle of triangle is 180° )

⇒ ∠BAC + 3k - 5 + 4k + 10 = 180°

⇒ ∠BAC + (3 × 23) - 5 + (4 × 23) + 10 = 180°

⇒ ∠BAC + 69 - 5 + 92 + 10 = 180°

⇒ ∠BAC + 166° = 180°

⇒ ∠BAC = 180° - 166°

   ∴ ∠BAC = 14°

Measure of ∠DAB is:

  ∠DAB = ∠DAC + ∠BAC

⇒ ∠DAB = 3k + 14°

⇒ ∠DAB = (3 × 23) + 14

⇒ ∠DAB = 69° + 14°

    ∴ ∠DAB = 83°