Math, asked by devanshisoni63, 1 year ago

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Answered by inhumandrowsey

In an equilateral triangle all angles are equal and sum of all the angles is 180°

So let the angle of triangle BEC = x

∠B + ∠E + ∠C = 180°

x + x + x = 180°

3x = 180°

x = 180°/3

x = 60°

So we get ∠B = ∠E = ∠C = 60°

Now as we get our ∠C = 60°

And we can see that the line AC passing through the mid point of side BE and intersecting at point C dividing ∠C in two equal parts.

So 1/2 of ∠C = 60°/2 = 30°

So measure of ∠BCP and ∠DCP will be equal = 30°

devanshisoni63: Thanks , this helps me a lot . Thanks again.

inhumandrowsey: No problem, i am here to help only. :)

devanshisoni63: I want to ask 2 more questions .

devanshisoni63: 1 st

devanshisoni63: Draw any rectangle and find the measure of angles at the four vertices made by the intersecting lines .

devanshisoni63: 2nd

devanshisoni63: If 2 lines intersect , do they always intersect at right angles ?

inhumandrowsey: Draw any rectangle and find the measure of angles at the four vertices made by the intersecting lines .
Answer: Since it is a rectangle then its opposite sides will be parallel to each other and all of the sides will be perpendicular so all the vertex angles will measure 90 degree and sum of all the angles will be 90+90+90+90 = 360

inhumandrowsey: If 2 lines intersect , do they always intersect at right angles ?
Not necessarily be true. If it is mentioned that two intersecting lines are perpendicular to each other then and only then you can say they intersect at right angles.

Answered by raja22praveen31

Let x be the equal angle of equilateral triangle.

In ΔABC,

∠A+∠B+∠C=180°

As, it is given that ,

∠A=∠B=∠C=x

⇒x+x+x = 180°

⇒3x = 180°

⇒x = 180°/3

⇒x=60°

Thus, the measure of each angle in an equilateral triangle = 60°

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