Ask Question
19 December, 13:00

In ΔABC, AD and BE are the angle bisectors of ∠A and ∠B and DE║ AB. Find the measures of the angles of ΔABC, if m∠ADE: m∠ADB = 2:9.

+4
Answers (1)
  1. 19 December, 14:11
    0
    Answer: ∠A=48°,∠B=48°,∠C=84°.

    Step by-step explanation:

    Given: AD and BE are the angle bisectors of ∠A and ∠B

    i. e ∠6=∠7 (∵ Angles formed after AD bisected ∠A)

    ∠4=∠5 (∵ Angles formed after BE bisected ∠B)

    Also, DE║AB

    ⇒ ∠2=∠7 (∵ Alternate interior angles)

    ∠3=∠6 (∵ Alternate interior angles)

    And ∠ADE : ∠ADB = ∠2:∠3 = 2:9 = 2x : 9x ... (1)

    To Find: ∠A,∠B,∠C.

    Solution: ∠2=∠7 (∵ Given) ... (2)

    ∠2=∠4 (∵ angles on the same segment) ... (3)

    ∠4=∠5 = ∠B/2 (∵ Given) ... (4)

    ∴ In Δ ABD

    ∠3+∠4+∠5+∠7 = 180 (∵ Sum of interior angles of a triangle)

    From equation 2,3,4,5, Put values

    9x+2x+2x+2x = 180°

    ⇒15x = 180°

    ⇒x=12°

    Putting values in equation (4) ⇒ ∠ B = 2 * (2*12) = 48°

    Also, ∠B=∠A=48°

    Now, in Δ ABC

    ∠C+∠B+∠A = 180°

    ⇒48°+48°+∠C = 180°

    ⇒∠C=84°
Know the Answer?
Not Sure About the Answer?
Get an answer to your question ✅ “In ΔABC, AD and BE are the angle bisectors of ∠A and ∠B and DE║ AB. Find the measures of the angles of ΔABC, if m∠ADE: m∠ADB = 2:9. ...” in 📙 Mathematics if there is no answer or all answers are wrong, use a search bar and try to find the answer among similar questions.
Search for Other Answers