Question

in triangle ABC a–b=15 & b–c=30 find a b& c​

Answer 1

》Right Question :

[Q]In triangle ABC /_A - /_B=15° & /_B - /_C=30°.Find /_A,/_B and /_C.

Answer:

$\huge{\pink{\green{\sf{\therefore \angle A=80\degree}}}}$

$\huge{\pink{\green{\sf{\therefore \angle B=65\degree}}}}$

$\huge{\pink{\green{\sf{\therefore \angle C=25\degree}}}}$

Step-by-step explanation:

$\huge{\pink{\green{\underline{\red{\sf{SOLUTION-}}}}}}$

• In question we have information and having three unknown and three eqn .

• According to given question :

$\: \: \: \: \: \: \: \: \: \: \: \: {\orange{ \underline{given}}} \\ { \green{ \angle A +\angle B +\angle C= 180 \degree}} \\ { \green{ \angle A - \angle B = 15\degree}} \\ { \green{ \angle B - \angle C = 30\degree}} \\ \\ { \red{ \underline{to \: find : }}} \\ { \purple{ \angle A=? }} \\ { \purple{ \angle B=? }} \\ { \purple{ \angle C =? }}$

$\to \angle A +\angle B +\angle C = 180 \degree - - - - - (1) \\ \to \angle A - \angle B= 15 \degree - - - - - (2) \\ \to \angle B - \angle C = 30 \degree - - - - - (3) \\ \\ adding \: (1) \: and \: (3) \\ \to \angle A +\angle B+\angle C +\angle B - \angle C = 180 \degree + 30 \degree \\ \to \angle A + 2\angle B= 210 \degree - - - - - (4) \\ \\ subtracting \: (2) \: from \: (1) \\ \to \angle A + 2\angle B - \angle B + \angle B = 210 \degree- 15 \degree \\ \to 3 \angle B= 195 \degree \\ { \green{\therefore \angle B = 65 \degree}} \\ \\ putting \: value \: of \angle B \: in \: (2) \\ \to \angle A - \angle B = 15 \degree \\ \to \angle A - 65 \degree = 15 \degree \\ \to \angle A = 15 \degree + 65 \degree \\ { \green{\therefore \angle A = 80 \degree}} \\ \\ putting \: value \: of \angle B \: in \: (3) \\ \to \angle B- \angle C= 30 \degree \\ \to 65 \degree - \angle C = 30 \degree \\ \to- \angle C = 30 \degree - 65 \degree \\ \to - \angle C = - 35 \degree \\ { \green{\therefore \angle C = 35 \degree}}$