Answer:
Step-by-step explanation:
Hello There!
So first things first
we need to find the measure of ∠ABD
If you didn´t know the sum of the triangle angles is 180
so to find ∠ABD we subtract the given angles ( 30 and 25) from 180
180-25-30=125
so angle ∠125
Now lets find ∠DBC
∠ABD and ∠ DBC are supplementary angles so the sum of the two angles is 180
So to find ∠DBC we subtract 125 from 180
180-125=55
so ∠DBC = 55
Now we can find the measure of ∠BDC
remember like stated before the sum of all of the angles in a triangle is 180
So to find the measure of ∠BDC we subtract the given angles from 180
180-90-55=35
so we could conclude that ∠BDC = 35
Other ways to solve for ∠DBC:
angle DBC is an exterior angle of ΔABD
the measure of an exterior angle is equal to the sum of the opposite interior angles
so basically ∠DBC = ∠ADB + ∠BAD
30+25=55 so ∠DBC = 55
Other ways to find angle BDC:
Having found the measure of ∠DBA and the other opposite angle we could find ∠BDC
Like stated before the measure of an exterior angle is equal to the sum of the opposite interior angles
basically ∠DBA = ∠BDC + ∠BCA
we have the measures of ∠BCA and ∠DBA so we plug in the values
125=∠BDC+90
isolate the variable by subtracting each side by 90
125-90=35
we´re left with
∠BDC=35
I hope this helps and if you have anymore questions, feel free to ask! :)
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