The measure of angle DBE is (0.1x - 22)° and the measure of angle CBE is (0.3x - 54)°. Find the value of x.

Question
Performing transformations
asked 2020-12-24
The measure of \angle DBE is (0.1x - 22)° and the measure of \angle CBE is (0.3x - 54)°. Find the value of x.

Answers (1)

2020-12-25
By Angle Addition Postulate,
\(\displaystyle{m}\angle{D}{B}{E}+{m}\angle{C}{B}{E}={m}\angle{D}{B}{C}\)
Since \(\displaystyle\angle{D}{B}{C}\) is a right angle as indicated by the square symbol, then \(\displaystyle{m}\angle{D}{B}{C}={90}°\). Hence,
\(\displaystyle{\left({0.1}{x}−{22}\right)}+{\left({0.3}{x}−{54}\right)}={90}\)
Solve for x:
\(\displaystyle{0.4}{x}−{76}={90}\)
\(\displaystyle{0.4}{x}={166}\)
\(\displaystyle{x}={\frac{{{166}}}{{{0.4}}}}\)
\(\displaystyle{x}={415}\)
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