Find the unknown marked angles in each of the following figures.......plz give answer with explanation......
Answers
Answer: Here's ur answer!
angle DBE+ k = 180 degree (linear pair)
=) 24+k=180
=) k=180-24
=) k= 156
now , angle DBA+angleDBE+ angle EBC = 180 degree ( straight line property)
=) h+24+k=180
=) h+24+156=180
=) h+180 = 180
=) h=0
So, value of k is 156 and value of h is 0
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Given :-
- AC || DF
- ∠BDE = 110°
- ∠DBE = 24°
To Find :-
The angle measurement of k and h.
Solution :-
Consider Δ BDE,
∠B = 24°
∠D = 110°
By applying angle sum property,
∠E = 180° - (110° + 24°)
⇒ ∠E = 180° - 134°
⇒ ∠E = 46°
Now,
∠E = k . . . (Alternate interior angles)
⇒ k = 46°
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k + 24° + h = 180° . . . (The angles lie on a straight line)
⇒ 46° + 24° + h = 180°
⇒ 70° + h = 180°
⇒ h = 180° - 70°
⇒ h = 110°
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◘ Note :- There are many ways of solving this question. Another method can be,
h and ∠BDE are alternate interior angles. So, h = 110°. Again by applying the straight line property, k becomes 46°.