Answered: "Geometry/trig help - having trouble finding an angle..."

tamkieuqf

Answered question

2022-08-11

Geometry/trig help - having trouble finding an angle

A B = A C

A D = B C

∠ B A C = 20^{\circ}

Find

α

pelvogp

Beginner2022-08-12Added 18 answers

Step 1
I'll leave out the degree symbol from my equations.
Let'd denote γ as the angle BDA. Then the angle

= 180 - γ

.
Let's also denote

β

as the angle DBC. From symmetry, we get that the angle ACB

= α + β

. Now, looking at the lower triangle, we obtain

(β) + (α + β) + (180 - γ) = 180 \Rightarrow α + 2 β - γ = 0

.
Step 2
From the upper triangle we get

20 + α + γ = 180 \Rightarrow α + γ = 160

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