In the given figure, AD is median and ∠ B = 350 and AB = AC then find the value of ∠BAD
Answers
Step-by-step explanation:
Given information:
AD is median,
AB=AC,
/_ABC or /_B =35°.
In triangle ABC, two sides of triangle are equal. It means triangle ABC is an isosceles triangle.
/_ADB=/_ADC=90° (AD is median)
In ∆ABD we have,
/_BAD + /_ABD =90°
/_BAD =90° - 35°
/_BAD = 55°
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Given:-
- AD is the median from vertex A to side BC
- ∠ABC = 35°
- AB = AC
To find:-
- Value of ∠BAD
Answer:-
As AB = AC, it means that △ABC is an isosceles triangle.
In △ADB and △ADC,
- AD = AD (Common)
- BD = CD. (AD is median)
- AB = AC (Given)
So, △ADB ≅ △ADC (SSS)
Hence, ∠ADB = ∠ADC ----( 1 ) (CPCTC)
Now,
BC is a line segment
∠ADB + ∠ADC = 180° (linear pair)
→ ∠ADB + ∠ADB = 180° [From ( 1 )]
→ 2∠ADB = 180°
→ ∠ADB = ∠ADC = 90° ----( 2 )
In △ADB,
- ∠ADB = 90° [From ( 2 )]
- ∠ABD = 35° [Given]
- ∠BAD = ?
We know that, in a triangle total angle is 180°
So,
∠ADB + ∠ABD + ∠BAD = 180°
→ 90° + 35° + ∠BAD = 180°
→ 125° + ∠BAD = 180°
→ ∠BAD = 180° - 125°
→ ∠BAD = 55° Ans.