The measure of ∠DBE is (0.1x−22)∘ and the measure of ∠CBE is (0.3x−54)∘. Find the value of x.

By the postulate of angle addition,m∠DBE+m∠CBE=m∠DBC&nbsp;Since&nbsp;∠DBC&nbsp;if the square sign indicates that it is a right angle, then&nbsp;m∠DBC=90°. Hence,&nbsp;(0.1x−22)+(0.3x−54)=90&nbsp;Solve for x:&nbsp;0.4x−76=90&nbsp;0.4x=166&nbsp;x=1660.4&nbsp;x=415

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High School
Geometry
High school geometry
Performing transformations

Clifland

Answered question

2020-12-24

The measure of $∠ D B E$ is $(0.1 x - 22)^{\circ}$ and the measure of $∠ C B E$ is $(0.3 x - 54)^{\circ}$ . Find the value of x.

Answer & Explanation

lamanocornudaW

Skilled2020-12-25Added 85 answers

By the postulate of angle addition,

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

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