Question

use the figure shown below to solve for x : figure not drawn to scale use your solution to find the measures of both angles. m∠abc = m∠cbd = enter an integer or decimal number more. question help: video message instructor

Explanation:

Step1: Set up angle - sum equation

Since $\angle ABC$ and $\angle CBD$ are complementary (form a right - angle, $90^{\circ}$), we have $8x+(7x + 30)=90$.

Step2: Combine like terms

Combining the $x$ terms on the left - hand side gives $15x+30 = 90$.

Step3: Isolate the variable term

Subtract 30 from both sides: $15x=90 - 30$, so $15x=60$.

Step4: Solve for x

Divide both sides by 15: $x=\frac{60}{15}=4$.

Step5: Find measure of $\angle ABC$

Substitute $x = 4$ into the expression for $\angle ABC$: $m\angle ABC=8x=8\times4 = 32^{\circ}$.

Step6: Find measure of $\angle CBD$

Substitute $x = 4$ into the expression for $\angle CBD$: $m\angle CBD=7x + 30=7\times4+30=28 + 30=58^{\circ}$.

Answer:

$x = 4$
$m\angle ABC = 32$
$m\angle CBD = 58$