Question

From the figure find the value of a, b, c, if () b= a+c and c= 2a. (2)find b if b = 2(a+c) ​

Answer 1

SOLUTION

TO DETERMINE

From the figure find the value of a, b, c, if

(1) b= a+c and c = 2a

(2) find b if b = 2(a+c)

EVALUATION

(1) It is given that b = a + c and c = 2a

∴ b = a + 2a = 3a

From the given figure

a + b + c = 180°

$\implies \sf{a + 3a + 2a = {180}^{ \circ} }$

$\implies \sf{6a = {180}^{ \circ} }$

$\implies \sf{a = {30}^{ \circ} }$

∴ a = 30° , b = 90° , c = 60°

(2) It is given that b = 2(a+c)

From the given figure

a + b + c = 180°

$\implies \sf{2a +2b + 2c = {360}^{ \circ} }$

$\implies \sf{2b + 2(a + c) = {360}^{ \circ} }$

$\implies \sf{2b + b = {360}^{ \circ} }$

$\implies \sf{3b = {360}^{ \circ} }$

$\implies \sf{b = {120}^{ \circ} }$

∴ b = 120°

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