Question

(b) In AABC, ZA + ZB = 65° and LB + C = 140° then find
each angle.​

Answer 1

Answer:

Answer

∠A+∠B=65

o

−−−(1)

∠A+∠C=140

o

−−−(2)

we know ∠A+∠B+∠C=180

o

from (1)65

o

+∠C=180

o

from (2)

∠C=115

o

from (2)

∠A+∠C=140

∠A+25=65

o

∠A=40

o

from (1)∠A+∠B=65

o

∠B=25

o

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Answer 2

Correct Question :-

In ∆ABC, ∠A + ∠B = 65° and ∠B + ∠C = 140°. Then find each angle.

Answer :-

• ∠A = 40°
• ∠B = 25°
• ∠C = 115°

Step-by-step explanation:

To Find :-

• The measure of all angles of triangle [∠A, ∠B and ∠C]

★ Solution

Given that,

→ ∠A + ∠B = 65°

→ ∠B + ∠C = 140°

Let us consider, ∠A + ∠B = 65° as equation 1.

∠A + ∠B = 65° ... equation (i)

And

∠B + ∠C = 140° as equation 2.

∠B + ∠C = 140° ... equation (ii)

We know,

Sum of all interior angles of triangle = 180°

∴ ∠A + ∠B + ∠C = 180°

By the problem,

⇒ ∠A + ∠B + ∠C = 180°

By putting the value of [∠A + ∠B = 65°], from equation (i)

⇒ 65° + ∠C = 180°

⇒ ∠C = 180° - 65°

⇒ ∠C = 115°

Finding ∠B from equation (ii)

⇒ ∠B + ∠C = 140°

⇒ ∠B + 115° = 140°

⇒ ∠B = 140° - 115°

⇒ ∠B = 25°

Now, finding ∠A from equation (i)

⇒ ∠A + ∠B = 65°

⇒ ∠A + 25° = 65°

⇒ ∠A = 65° - 25°

⇒ ∠A = 40°

Hence,

The measure of ∠A, ∠B and ∠C is 40°, 25° and 115° respectively.