Question

1. In the figure below ABC∡=153°, ABD∢=(5x+5)°, and DBC∢=(3x+12)°. Find the measure of ABD∢ and DBC∢. Show all work

Answer 1

 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 = $\frac{136}{8}$

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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