What is the m∠abc?
m∠abc = 60°, m∠abc = 67°, m∠abc = 120°, m∠abc = 127°

Solution:

From the figure,

m∠BCD = 67°

m∠BDC = 60°

We have to find the value of m∠abc.

We know, the sum of interior angles is always equal to 180°

So, m∠CBD + m∠BCD + m∠BD = 180°

m∠CBD + 67 + 60 = 180°

m∠CBD + 127 = 180°

m∠CBD = 180° - 127°

m∠CBD = 63°

We know, m∠ABC + m∠CBD = 180°[linear pair of angles]

m∠ABC + 63° = 180°

m∠ABC = 180° - 63°

m∠ABC = 127°

Therefore, the value of m∠ABC is 127°

Aliter:

From the figure,

m∠BCD = 67°

m∠BDC = 60°

We have to find the value of m∠abc. This is the exterior angle formed.

According to the exterior angle theorem, the exterior angle of a triangle formed is equal to the sum of the measures of the two opposite interior angles of the triangle.

m∠ABC = m∠BCD + m∠BDC

= 67°+ 60°

=127°