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# In a triangle, ABC, AD bisects angle BAC and AD = DC. If

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In a triangle, ABC, AD bisects angle BAC and AD = DC. If [#permalink]  12 Mar 2005, 09:06
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In a triangle, ABC, AD bisects angle BAC and AD = DC. If angle BDA = 75 degress, angle ACD measure (in degrees)

a) 37.5
b) 67.5
c) 70.5
d) 72.5
e) 73

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A - 37.5

Since AD = DC, we know that ADC is an isoceles triangle and that angle DAC = DCA.

Also, since we know that BDA = 75 degrees, CDA = 105 degrees.

Since all triangles must equal 180 degrees, it follows that DAC + DCA = 75 degrees, or DAC = DCA = 37.5 degrees.
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A
1. Since Sides are equal so the angles will be equal. <DAC = <ACD
2. Sum of opposite angles equals to the exterior angle.

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