Thus the measure of ∠DBC is 31.
Given,
m∠ABD=4x+23 and m∠DBC=4x−5.
We need to find what is the measure of m∠DBC.
We have,
The given figure is a 90-degree angle.
So,
m∠ABC = m∠ABD + m∠DBC _______(A)
We have,
m∠ABD=4x+23
m∠DBC=4x−5
m∠ABC = 90
Substituting in (A)
We get,
m∠ABC = m∠ABD + m∠DBC
90 = 4x + 23 + 4x - 5
90 = 8x + 18
Subtracting 8 on both sides.
90 - 18 = 8x + 18 - 18
72 = 8x
Dividing 8 into both sides.
72/8 = 8x/8
9 = x
x = 9
Putting x = 9 in ∠DBC=4x−5.
∠DBC = 4x−5
= 4x9 - 5
= 36 - 5
= 31
Thus the measure of ∠DBC is 31.
Learn more about finding the measure of a given angle here:
https://brainly.com/question/16689519
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