2 answers:
Answer:
<u>∠ABD = 43°</u>
Step-by-step 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°
⇒ <u>∠ABD = 43°</u>
Answer:
As ΔABC is an <u>isosceles triangle</u>:
⇒ BA = BC
(the dashes on the line segments indicate they are of equal measure)
⇒ ∠BAC = ∠BCA = 55°
⇒ ∠BCA = ∠BAD = 55°
Angles on a <u>straight line</u> sum to 180°
⇒ ∠ADE + ∠EDC = 180°
⇒ 98° + ∠EDC = 180°
⇒ ∠EDC = 82°
As BE intersects AC, the <u>vertically opposite angles</u> are <em>equal</em>:
⇒ ∠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°
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