Dealing with angles (2)

Geometry Level 3

Knowing that all angles in degrees, and d > c d > c which one is greater a a or d − b d-b ?

d − b > a d - b > a Insufficient Information a = d − b a = d - b a > d − b a > d-b

Hana Wehbi by Hana Wehbi , 51, USA

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2 solutions

Áron Bán-Szabó
Jul 12, 2017

Note that in a triangle the sum of any two angle is equal to the third angle's exterior angle. So a + b = c < d ⟹ a + b − b < d − b ⟹ a < d − b a+b=c<d \Longrightarrow a+b-b<d-b \Longrightarrow a<d-b .

Therefore the answer is ( d − b ) \boxed{(d-b)} .

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Thank you.

Hana Wehbi - 3 years, 11 months ago
Chew-Seong Cheong
Jul 13, 2017

c = a + b ⟹ c − b = a Since d > c d − b > a \begin{aligned} c & = a + b \\ \implies {\color{#3D99F6}c} - b & = a & \small \color{#3D99F6} \text{Since }d > c \\ {\color{#3D99F6}d} - b & > a \end{aligned}

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Thank you.

Hana Wehbi - 3 years, 11 months ago

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