Question

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Answer 1

∠ABD = 43°

Explanation:

Let's solve !

⇒ ∠BAC = ∠BCA = 55° (Angles opposing equal sides)

⇒ ∠BDA = 180° - 98° (Linear pair)

⇒ ∠BDA = 82°

⇒ ∠BAC + ∠BDA + ∠ABD = 180° (Angle Sum Property)

⇒ ∠ABD + 82° + 55° = 180°

⇒ ∠ABD + 137° = 180°

⇒ ∠ABD = 43°

Answer 2

As ΔABC is an isosceles triangle:

⇒ BA = BC
(the dashes on the line segments indicate they are of equal measure)

⇒ ∠BAC = ∠BCA = 55°

⇒ ∠BCA = ∠BAD = 55°

Angles on a straight line sum to 180°

⇒ ∠ADE + ∠EDC = 180°

⇒ 98° + ∠EDC = 180°

⇒ ∠EDC = 82°

As BE intersects AC, the vertically opposite angles are equal:

⇒ ∠BDC = ∠ADE = 98°

⇒ ∠ADB = ∠EDC = 82°

Interior angles in a triangle sum to 180°

⇒ ∠BAD + ∠ADB + ∠ABD = 180°

⇒ 55° + 82° + ∠ABD= 180°

⇒ ∠ABD = 180° - 55° - 82°

⇒ ∠ABD = 43°