Question

What is the measure of ∠ABD?

Answer 1

m∠ABD = 114°

Explanation:

Given measurements of interior angles are:

m∠D = 2n°

m∠C = 60°

m∠ABD = (4n+6)°

The measurement of exterior angle of a triangle is equal to the sum of two opposite interior angles.

This can be mathematically expressed as:

m∠ABD = m∠C+m∠D

Putting the respective values

`4n+6 = 2n+60\\4n-2n+6 = 60\\2n+6 = 60\\2n = 60-6\\2n = 54\\(2n)/(2) = (54)/(2)\\n = 27`

Putting n=27 in (4n+6)°

`=4(27) + 6\\= 108+6 = 114`

Hence,

m∠ABD = 114°