∆ ABC, ∠A +∠B = 116° and ∠B + ∠C = 126°. The measure of an

1.	∆ ABC, ∠A +∠B = 116° and ∠B + ∠C = 126°. The measure of angles ∠A, ∠B and ∠C are
Answer» To find :- we NEED to find measure of angles ∠A, ∠B and ∠C Solution : ∠A +∠B = 116° .....1) ∠B + ∠C = 126° ......2) From equation (1) ⠀⠀⠀⠀⠀⠀∠A +∠B = 116 ⠀⠀⠀⠀⠀⠀∠B = 116 - ∠A .....3) From equation (2) ⠀⠀⠀⠀⠀⠀∠B + ∠C = 126° ⠀⠀⠀⠀⠀⠀116 - ∠A + ∠C = 126° ⠀⠀⠀⠀⠀⠀∠C - ∠A = 126 - 116 ⠀⠀⠀⠀⠀⠀∠C = 10 + ∠A ....(4) We know that, ♻️Sum of all angles of triangle = 180 So, ∠A + ∠B + ∠C = 180 From (3) and (4) ⟶ ∠A + (116 - ∠A) + 10 + ∠A = 180 ⟶ ∠A + 116 - ∠A + 10 + ∠A = 180 ⟶ ∠A + 126 = 180 ⟶ ∠A = 180 - 126 ⟶ ∠A = 54 So, ⇝∠B = 116 - ∠A ⇝∠B = 116 - 54 ⇝∠B = 62 And ›› ∠C = 10 + ∠A ›› ∠C = 10 + 54 ›› ∠C = 64 Hence, Measure of all angles of ∆ABC are :- ∠A = 54 ∠B = 62 ∠C = 64 Verification :- Sum of all angles of triangle = 180 ››➔ ∠A + ∠B + ∠C = 180 ››➔ 54 + 62 + 64 = 180 ››➔ 54 + 126 = 180 ››➔ 180 = 180 LHS = RHS Hence VERIFIED. ━━━━━━━━━━━━━━━━━━━━━━━━━

∆ ABC, ∠A +∠B = 116° and ∠B + ∠C = 126°. The measure of angles ∠A, ∠B and ∠C are

Answer»

To find :-

we NEED to find measure of angles ∠A, ∠B and ∠C

Solution :

∠A +∠B = 116° .....1)
∠B + ∠C = 126° ......2)

From equation (1)

⠀⠀⠀⠀⠀⠀∠A +∠B = 116

⠀⠀⠀⠀⠀⠀∠B = 116 - ∠A .....3)

From equation (2)

⠀⠀⠀⠀⠀⠀∠B + ∠C = 126°

⠀⠀⠀⠀⠀⠀116 - ∠A + ∠C = 126°

⠀⠀⠀⠀⠀⠀∠C - ∠A = 126 - 116

⠀⠀⠀⠀⠀⠀∠C = 10 + ∠A ....(4)

We know that,

♻️Sum of all angles of triangle = 180

So,

∠A + ∠B + ∠C = 180

From (3) and (4)

⟶ ∠A + (116 - ∠A) + 10 + ∠A = 180

⟶ ∠A + 116 - ∠A + 10 + ∠A = 180

⟶ ∠A + 126 = 180

⟶ ∠A = 180 - 126

⟶ ∠A = 54

So,

⇝∠B = 116 - ∠A

⇝∠B = 116 - 54

⇝∠B = 62

And

›› ∠C = 10 + ∠A

›› ∠C = 10 + 54

›› ∠C = 64

Hence,

Measure of all angles of ∆ABC are :-

∠A = 54
∠B = 62
∠C = 64

Verification :-

Sum of all angles of triangle = 180

››➔ ∠A + ∠B + ∠C = 180

››➔ 54 + 62 + 64 = 180

››➔ 54 + 126 = 180

››➔ 180 = 180

LHS = RHS

Hence VERIFIED.

━━━━━━━━━━━━━━━━━━━━━━━━━