Question

use the image below to find the requested values. find the measure of ∠tdc.

Explanation:

Step1: Note angle - sum property

The sum of angles $\angle FDC$ and $\angle TDC$ is a right - angle (90°) since there is a right - angle symbol at $\angle FDT$.

Step2: Set up equation

We know that $\angle FDC = 54^{\circ}$ and $\angle TDC=4y^{\circ}$, and $\angle FDC+\angle TDC = 90^{\circ}$. So, $54 + 4y=90$.

Step3: Solve for $y$

Subtract 54 from both sides of the equation: $4y=90 - 54$. So, $4y = 36$. Then divide both sides by 4: $y=\frac{36}{4}=9$.

Step4: Find measure of $\angle TDC$

Since $\angle TDC = 4y^{\circ}$ and $y = 9$, then $\angle TDC=4\times9^{\circ}=36^{\circ}$.

Answer:

$36^{\circ}$