Math, asked by anshikachikkara, 1 year ago

In triangle abc angle a+angle b = 65 degree and angle b + angle c = 140 degree then find the measure of each of the angle

Answers

Answered by MADÇŘÊÅȚÜŔĒ

It must be the right answer

Attachments:

MADÇŘÊÅȚÜŔĒ: In the 1st part we assume angle A+angle B=65 as equation(¡) and angleB+angle C=104 as equation (¡¡)

anshikachikkara: then tell me how the angle b come

MADÇŘÊÅȚÜŔĒ: we add both equation (¡)and (¡¡), and by adding this we get angle B

anshikachikkara: then tell me how the sum of angle a+b+ c is 180 degree according to the question

anshikachikkara: according to your solution

MADÇŘÊÅȚÜŔĒ: this is because the sum of all angles of a triangle is 180 degree

anshikachikkara: still I can't understand the solution after 4th step

MADÇŘÊÅȚÜŔĒ: by this we have taken out the value of angle B and we put the value of angle B in equation (¡)and (¡¡) and by this we found angle A and angleB

anshikachikkara: thank you

anshikachikkara: hii

Answered by arindamvutla

The measures of the angles are:

∠a = 40°

∠b = 25°

∠c = 115°

Step-by-step explanation:

Given:

∠ a + ∠ b = 65°--------- 1

∠ b + ∠ c = 140°-------- 2

Adding equations (1) and (2), we get:

∠ a + ∠ b + ∠ b + ∠ c = 65 + 140

(∠ a + ∠ b + ∠ c) + ∠ b = 205 --------- 3

We know that, sum of all the interior angles of a triangle is 180°.

So, ∠ a + ∠ b + ∠ c = 180°

Plug in 180 for ∠ a + ∠ b + ∠ c in equation 3. This gives,

180 + ∠ b = 205

∠ b = 205 - 180

∠ b = 25°.

Now, from equation (1),

∠ a = 65° - ∠ b

∠ a = 65° - 25° = 40°

Now, from equation (2),

∠ c = 140° - ∠ b

∠ c = 140° - 25° = 115°

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