Question

.

Find m∠ABC.




60°


23°


30°


53°

Answer 1

The value of angle ∠ ABC is 30°

Explanation:

Given as shown in fig :

∠ ABC = ( x + 7 )°

∠ CBD = ( 2x + 14 )°

∵ From figure ,

∠ ABD = 90°

And ∠ ABD = ∠ ABC + ∠ CBD

I.e 90° = ( x + 7 )° + ( 2x + 14 )°

Or, 90° = (3x)° + 21°

Or, 90° - 21° = (3x)°

Or, 69° = (3x)°

∴ x =
`(69)/(3)` = 23°

So, ∠ ABC = ( x + 7 )° = 23° + 7° = 30°

And ∠ CBD = ( 2x + 14 )° = (2×23)° + 14°

Or, ∠ CBD = 60°

Hence The value of angle ∠ ABC is 30° Answer