Question

find the measure of x and the measure of each angle

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Answer 1

Answer :

x = 2

∠BCD = 10°

∠BDC = 13°

∠ABD = 23°

∠CBD = 157°

Note :

★ Sum of all the three interior angles of a triangle is 180° .

★ Sum of any two interior angles of a triangle is equal to its opposite exterior angle .

Solution :

Given : ∠BCD = (4x + 2)°

∠BDC = (2x + 9)°

∠ABD = (5x + 13)°

To find : x = ?

∠BCD = ?

∠BDC = ?

∠ABD = ?

∠CBD = ?

We know that ,

Sum of any two interior angles of a triangle is equal to its opposite exterior angle .

Thus ,

=> ∠BCD + ∠BDC = ∠ABD

=> 4x + 2 + 2x + 9 = 5x + 13

=> 6x + 11 = 5x + 13

=> 6x - 5x = 13 - 11

=> x = 2

Thus ,

=> ∠BCD = (4x + 2)°

=> ∠BCD = (4•2 + 2)°

=> ∠BCD = (8 + 2)°

=> ∠BCD = 10°

Also ,

=> ∠BDC = (2x + 9)°

=> ∠BDC = (2•2 + 9)°

=> ∠BDC = (4 + 9)°

=> ∠BDC = 13°

Also ,

=> ∠ABD = (5x + 13)°

=> ∠ABD = (5•2 + 13)°

=> ∠ABD = (10 + 13)°

=> ∠ABD = 23°

Also ,

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

Thus ,

=> ∠BCD + ∠BDC + ∠CBD = 180°

=> 10° + 13° + ∠CBD = 180°

=> 23° + ∠CBD = 180°

=> ∠CBD = 180° - 23°

=> ∠CBD = 157°

Hence ,

x = 2

∠BCD = 10°

∠BDC = 13°

∠ABD = 23°

∠CBD = 157°