Question

If an angle of 130° is bisected, find the measure of each angle formed.​

Answer 1

Step-by-step solution:

Consider a △ABC,such that ∠BAC=130∘ and bisectors of ∠B and ∠C meet at O.

To find: ∠BOC

Now, in △ABC,

∠BAC+∠ABC+∠ACB=180

130+∠ABC+∠ACB=180 (Angle sum property)

∠ABC+∠ACB=50

21(∠ABC+∠ACB)=25

∠OBC+∠OCB=25 (OB and OC bisect ∠ABC and ∠ACB)

Now, in △OBC,

∠OBC+∠OCB+∠BOC=180

25+∠BOC=180

∠BOC=155∘.

Answer 2

Answer:

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Step-by-step explanation:

What is the solution to this problem: if one of the angles of a triangle is 130 degrees, what would be the angle between the bisector of the other

10 Answers



Girija Warrier, studied at Sufficiently Educated

Answered 3 years ago · Author has 3.4K answers and 6.1M answer views



GIVEN: Angle A = 130°

TO FIND : Angle DPE = Angle CPB =?

Let angle B be 2x

So, angle C = 180 - (130 +2x) = 50–2x

So angle DCB =(50–2X)/2

Now, angle CDA = 2x + (50–2x)/2 ( as exterior angle = the sum of 2 opposite interior angles)

=> angle CDA = (2x +50)/2 = x+ 25 ……..(1)

Now,in triangle AEB, angle AEB =180 - (130+x) = 50 -x ………….(2)

So, in quadrilateral ADPE,

angle DPE = 360 -(130 + x+25 + 50-x)

=> angle DPE = 360- 205

=> angle DPE = 155°