Geometry Level 2

Given that BY = BA , CX = CA , and angle XAY = 43° , find the angle BAC.

The answer is 94.

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3 solutions

Kenny Lau
Jul 4, 2014

(X refers to \angle AXY and Y to \angle AYX, all numeric values unspecified are angles)

Since AXY is a triangle (yds), 43+X+Y=180, X+Y=137.

\angle BAY = Y \rightarrow \angle BAX = Y-43

\angle CAX = X \rightarrow \angle CAY = X-43

Therefore \angle BAC

= \angle BAX + \angle XAY + \angle YAC

=X-43 + 43 + Y-43




So triangle AXY is not isoceles?

Jia O. - 6 years, 11 months ago

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It is not given, and one shall not assume it.

Kenny Lau - 6 years, 11 months ago

nice method!

Shourya Gupta - 6 years, 6 months ago
Rifath Rahman
Jul 4, 2014

As BY=BA so in ABY <BAY=<AYB let BAY=43+x so in ABY <BAY+<AYB+<B=180 or <BAY+<BAY+<B=180 or 2<BAY+<B=180 or 2(43+x)+<B=180 or 86+2x+<B=180 or <B=94-2x..........(1) Now as CX=CA,so in AXC <AXC=<XAC let <XAC=43+y then in AXC <AXC+<XAC+ <C=180 or 2<XAC+<C=180 or 2(43+y)+<C=180 or 86+2y+<C=180 or <C=94-2y..............................................(2) Now in the whole ABC <A+<B+<C=180 or x+43+y+94-2x+94-2y=180 (putting the value of (1) and (2) or 231-x-y=180 or 231-180=x+y or x+y=51 so <BAC=<A=x+43+y=x+y+43=51+43=94

Jia O.
Jul 1, 2014

Anyone has solution? Needed…~

Posted a solution. ^_^

Kenny Lau - 6 years, 11 months ago

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