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By angle addition postulate,
m(∠ABD) + m(∠DBC) = m(∠ABC)
Now substitute the values of each angle,
(5x + 5)° + (3x + 12)° = 153°
Combine like terms of the expression,
(5x + 3x) + (5 + 12) = 153
8x + 17 = 153
8x = 153 - 17
x =
x = 17
Substitute the value of 'x' to get the measure of each angle,
m(∠ABD) = (5x + 5)
= 5(17) + 5
= 90°
m(∠DBC) = (3x + 12)
= 3(17) + 12
= 63°
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Answer:
132°
Step-by-step explanation:
Quadrilateral ABCD is inscribed in a circle,
So, it is a cyclic quadrilateral.
Opposite angles of a cyclic quadrilateral are supplementary.
(3x-12)° = (3*48 - 12)° = (144 - 12)° = 132°