if angle A+angle B=120degree and angle C+angle B=110degree find angle ABC
Answers
Answer:
Answer
It is given that ∠A+∠B=125
∘
…(1)
We know that the sum of all the angles in a triangle is 180
∘
.
So we can write it as
∠A+∠B+∠C=180
∘
By substituting ∠A+∠B=125
∘
in the above equation
125
∘
+∠C=180
∘
On further calculation
∠C=180
∘
−125
∘
By subtraction
∠C=55
∘
It is given that ∠A+∠C=113
∘
By substituting the value of ∠C
∠A+55
∘
=113
∘
On further calculation
∠A=113
∘
−55
∘
By subtraction
∠A=58
∘
By substituting ∠A=58
∘
in equation (1)
So we get
∠A+∠B=125
∘
58
∘
+∠B=125
∘
On further calculation
∠B=125
∘
−58
∘
By subtraction
∠B=67
∘
Therefore, ∠A=58
∘
,∠B=67
∘
and ∠C=55
∘
.
Step-by-step explanation:
I HOPE IT HELP YOU
Step-by-step explanation:
Let angle A be 110
and angle B be 2a
So angle C will be 180–110–2a ———angle sum
Angle C is 70–2a
Let angle between 2 angle bisectors be x
Assuming the bisector is internal angle bisector
2a÷2 + (70–2a)÷2 + x =180
x=180-a - (35-a)
Solving, we get x = 155°