Question

1. in the diagram below, ∠abc is a right angle. if m∠abd = 13x and m∠dbc = 9x + 2, find the measure of ∠dbc.

Explanation:

Step1: Set up equation based on angle - sum

Since $\angle ABC$ is a right - angle ($90^{\circ}$) and $\angle ABC=\angle ABD+\angle DBC$, we have the equation $13x+(9x + 2)=90$.

Step2: Combine like terms

Combining the $x$ terms on the left - hand side gives $(13x+9x)+2 = 90$, which simplifies to $22x+2 = 90$.

Step3: Isolate the variable term

Subtract 2 from both sides of the equation: $22x+2 - 2=90 - 2$, resulting in $22x=88$.

Step4: Solve for $x$

Divide both sides by 22: $x=\frac{88}{22}=4$.

Step5: Find the measure of $\angle DBC$

Substitute $x = 4$ into the expression for $\angle DBC$. So, $m\angle DBC=9x + 2=9\times4+2=36 + 2=38$.

Answer:

$38$