Clifland

2020-12-24

The measure of $\mathrm{\angle }DBE$ is $\left(0.1x-22{\right)}^{\circ }$ and the measure of $\mathrm{\angle }CBE$ is $\left(0.3x-54{\right)}^{\circ }$. Find the value of x.

lamanocornudaW

Expert

By the postulate of angle addition,

$m\mathrm{\angle }DBE+m\mathrm{\angle }CBE=m\mathrm{\angle }DBC$
Since $\mathrm{\angle }DBC$ if the square sign indicates that it is a right angle, then $m\mathrm{\angle }DBC=90°$. Hence,
$\left(0.1x-22\right)+\left(0.3x-54\right)=90$
Solve for x:
$0.4x-76=90$
$0.4x=166$
$x=\frac{166}{0.4}$
$x=415$

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