Find the value of k. I want with steps
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Answers
Step-by-step explanation:
Solution :-
Method-1:-
Let consider a triangle ABC and triangle CDE.
In ∆ ABC,
<CAB = 30°
<ABC = 34°
We know that
The sum of all angles in a triangle is 180°
=> < CAB + <ABC + <BCA = 180°
=> 30°+34°+<BCA = 180°
=> 64° + <BCA = 180°
=> <BCA = 180°-64°
=> <BCA = 116°
and
<BCA and <ACD are linear pair.
=> <BCA + <ACD = 180°
=> 116°+<ACD = 180°
=> < ACD = 180°-116°
=> < ACD = 64°
and
<ACD =<ECD
In ∆ CDE,
< CDE + <DEC + <ECD = 180°
=> 45° + <DEC + 64° = 180°
=> <DEC + 109° = 180°
=> <DEC= 180°-109°
=> <DEC = 71°
Now,
<DEC + <DEA = 180°
=> 71°+k = 180°
=> k = 180°-71°
=> k = 109°
Therefore, k = 109°
Method-2:-
Let consider a triangle ABC and triangle CDE.
In ∆ ABC,
<CAB = 30°
<ABC = 34°
<ECD is the exterior angle.
We know that
An exterior angle is equal to the sum of the two opposite interior angles
=> <ECD = <CAB + <ABC
=> <ECD = 30°+34°
=> <ECD = 64°
Now,
<AED is the exterior angle.
We know that
An exterior angle is equal to the sum of the two opposite interior angles
=> <AED = <ECD + <CDE
=> k = 64°+45°
=> k = 109°
Therefore, k = 109°
Answer:-
The value of k for the given problem is 109°
Used formulae:-
→ The sum of all angles in a triangle is 180°
→ An exterior angle is equal to the sum of the two opposite interior angles in a triangle.
→ The sum of two adjacent angles is equal to 180° is called Linear pair.
Step-by-step explanation:
given :
- find the value of k 30 degree 34 degree 45 degree
to find :
- 30 degree 34 degree 45 degree
solution :
- the answer is
- 45 - 34
- 11 degree
= 11 degree
