a
11. Show that Angle ABC is isosceles if
(i) A = 70° and B = 40°.
(ii) B = 30° and C = 120°.
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Answer:
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Step-by-step explanation:
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△ABC is an isosceles triangle in which AB=AC. Sides BA is produced to D such that AD=AB. Show that ∠BCD is a right angle.
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In △ABC, we have
AB=AC ∣ given
∠ACB=∠ABC ... (1) ∣ Since angles opp. to equal sides are equal
Now, AB=AD ∣ Given
∴AD=AC ∣ Since AB=AC
Thus , in △ADC, we have
AD=AC
⇒∠ACD=∠ADC ... (2) ∣ Since angles opp. to equal sides are equal
Adding (1) and (2) , we get
∠ACB+∠ACD=∠ABC+∠ADC
⇒∠BCD=∠ABC+∠BDC ∣ Since∠ADC=∠BDC
⇒∠BCD+∠BCD=∠ABC+∠BDC+∠BCD ∣ Adding ∠BCD on both sides
⇒2∠BCD=180
∘
∣ Angle sum property
⇒∠BCD=90
∘
Hence, ∠BCD is a right angle.
Answer:
C=120°
Step-by-step explanation:
In the isosceles triangle one of the angle is more than 90°
That means angle one of the angle in triangle ABC is more than 90°
So angle C in more than 90°
So option C is correct