Triangles!

Geometry Level 3

In triangle ABC , a point D is on Line AC so that AB = AD so that measure of angle ABC minus measure of Angle ACB = 45 degrees. Find measure of Angle CBD


The answer is 22.5.

Samuel Cuadra by Samuel Cuadra , 21, Philippines

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1 solution

Md Zuhair
Oct 5, 2016

In this problem we see from the figure that A B C ABC = x + z x +z and A C B ACB = x − z x-z , And it is given that A B C ABC - A C B ACB = 45 45 . Then x + z − ( x − z ) = 45 x+z - (x-z) = 45

= > 2 z = 45 => 2z = 45 . Then z = 22.5 z= 22.5 . And From the figure we know z = C B D = 22.5 z= CBD = 22.5 . (ANS)

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Blegh... i read this problem wrong. Came out on 45 degrees. Which seemed unlikely because then BAD would have ben 90 degrees.

Peter van der Linden - 4 years, 8 months ago

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it could be, because the problem did not stated that the triangle is a Scalene triangle, or not an Equi. Right Triangle, so anything is possible

Samuel Cuadra - 4 years, 8 months ago

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