Question

Use the diagram and information below to choose the correct equation to solve for x.

m< ABD = x + 67

m<DBC= x + 51

m<ABC = 104

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Responses

x + 67 + 104 = x + 51
x + 67 + 104 = x + 51

x + 67 = 104 + x + 51
x + 67 = 104 + x + 51

x + 67 + x + 51 = 104
x + 67 + x + 51 = 104

x + 51 + 104 + x + 51 = 180

Answer 1

m∠ABD and m∠DBC are adjacent and add to m∠ABC, so

(x + 67) + (x + 51) = 104.

(You can simplify: 2x + 118 = 104 ⇒ 2x = −14 ⇒ x = −7.)