The measure of angles are
i) Angle ABD = 67°
ii) Angle CBD = 67°
iii) Angle ABC = 134°
We have been given that ray BD bisects angle ABC and also
Angle ABC = (25x+34)°
Angle CBD = (11x + 23)°
Note that angle ABC = angle ABD + angle CBD (1)
And angle ABD = angle CBD = (11x + 23)° as it is bisected into two equal half.
Therefore putting the required values of angle in equation (1) we get
(25x+34)° = 2(11x+23)°
25x+34 = 22x+46
25x – 22x = 46 – 34
3x = 12
x = 4
Hence, angle ABD = (11*4 + 23) ° = 44+23 = 67°
Angle CBD = (11*4 + 23) ° = 44+23 = 67°
angle ABC = (25*4 + 34)° = 100+34 = 134°
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