Find the measure of /abd

a.71
b.109
c. 119
d.132

Option C. 119°

Step-by-step explanation:

In the given triangle BCD, ∠DBC = 61° and ∠BDC = 48° are given.

We have to calculate the measure of ∠ ABD.

Since ∠ABD + ∠DBC = 180° [ supplementary angles ]

Therefore ∠ABD + 61° = 180°

∠ABD = 180° - 61°

∠ABD = 119°

We should not get confused with the measures of other angles given.

Option C. 119° is the measure of ∠ ABD

geometry: triangles

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answers archive

call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

25.45584

so, converting firstly the mixed fractions to improper fractions and then "adding".