Problem

13. If $\overrightarrow{B D} \perp \overrightarrow{A C}, m \angle D B E=(2 x-1)^{\circ}$, and $m \angle C B E=(5 x-42)^{\circ}$, find the value of $x$. 14. Find th $m \angle P Q$ P $Q$ 15. Find the values of $x$ and $y$.

Solution

Step 1 :Given that $\overrightarrow{B D} \perp \overrightarrow{A C}$, $m \angle D B E=(2 x-1)^{\circ}$, and $m \angle C B E=(5 x-42)^{\circ}$, we know that $\angle DBE$ and $\angle CBE$ are supplementary angles, meaning their measures add up to 180 degrees.

Step 2 :Set up the equation $(2x - 1) + (5x - 42) = 180$ and solve for $x$.

Step 3 :Solving the equation gives $x = \frac{223}{7}$.

Step 4 :Final Answer: The value of $x$ is $\boxed{\frac{223}{7}}$.

From Solvely APP
Source: https://solvelyapp.com/problems/KVMTl2aLdb/

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