If two angles form a large angle when combined, they will follow the angle addition postulate.
Measure of ∠ABD is 90° and the measure of ∠DBC will be 63°.
From the figure attached.
- Two angles ∠ABD and ∠DBC are formed at a point B.
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 = [tex]\frac{136}{8}[/tex]
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°
Therefore, m(∠ABD) = 63° and m(∠DBC) = 63° will be the answer.
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