![3300](/avatars/27126.jpg)
3300
22.06.2019 •
Mathematics
3x - y = 13 2x+4y= - 22 elimination
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Ответ:
Ответ:
The measure of ∠A is 32°.
Step-by-step explanation:
Given : AB = BC
∠BEC=90°
∠DCE=42°
CD bisects ∠ACB :
∠ACD = ∠DCB = x
∠DCE= ∠BCE + ∠DCB = ∠BCE + x = 42°
To find : ∠A = ?
Solution:
InΔ ACE:
∠A +∠E +∠ACD + ∠DCB + ∠BCE = 180° (Angle sum property)
∠A +∠E +∠DCB + ∠DCB + ∠BCE = 180°
∠A +∠E +x + x + ∠BCE = 180°
∠A +∠E + x + 42° = 180°
∠A + x = 180° - 90° - 42° = 48°
∠A + x = 48°...[1]
In Δ ABC
AB = BC (given)
Hence, Isosceles triangle
∠A = ∠ACB = 2x ..[2]
(Angle opposite to equal sides are equal)
Using [2] in [1] we get:
2x + x = 48°
x = 16°
∠A = 2x = 2 × 16° = 32°