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n200080 [17]
3 years ago
6

What is the measure of ∠ABD?

Mathematics
1 answer:
Ad libitum [116K]3 years ago
4 0

Answer:

m∠ABD = 114°

Step-by-step 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\\\frac{2n}{2} = \frac{54}{2}\\n = 27

Putting n=27 in (4n+6)°

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

Hence,

m∠ABD = 114°

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