There room two instances in this geometry problem. In the very first case, the worth of \$x\$ is given and also it is \$25^\circ\$ yet the value of \$y\$ is unknown. In the 2nd case, the worth of \$x\$ is unknown however the value of \$y\$ is given and it is \$35^\circ\$.

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However, there is a geometrical relation between the literals \$x\$ and also \$y\$ as presented in the image. Let us an initial find the relation in between theme and then the same relation offered to uncover the worths of variables in both cases.

Relation

\$\overleftrightarrowAB\$ is a right line and its middle suggest is \$O\$. We understand that, the edge of a right line is always \$180^\circ\$ geometrically.

\$\therefore \,\,\,\,\,\, \angle AOB = 180^\circ\$.

The ray \$\overrightarrowOC\$ is started from suggest \$O\$. It provides \$3x^\circ\$ angle through \$\overrightarrowOB\$ heat and additionally makes \$(2y+5)^\circ\$ angle with \$\overrightarrowOA\$ ray.

Therefore, \$\angle COB = 3x^\circ\$ and also \$\angle COA = (2y+5)^\circ\$.

Geometrically, the angle \$AOB\$ is equal to the amount of the angles \$COA\$ and \$COB\$.

\$\therefore \,\,\,\,\,\, \angle AOB = \angle COA + \angle COB\$

\$\implies \angle COA + \angle COB = \angle AOB\$

\$\implies (2y+5)^\circ + 3x^\circ = 180^\circ\$

The mathematical an interpretation of \$x^\circ\$ in the term \$3x^\circ\$ is the worth of \$x\$ is in degrees. Remember it and also just compose it as \$x\$ in the equation. Therefore, the product the number \$3\$ and \$x\$ provides an angle in degrees.The definition of the expression \$(2y+5)^\circ\$ is an angle in degrees. It is actually developed by the sum of the terms \$2y\$ and also \$5\$. If the worth of the expression \$(2y+5)^\circ\$ is in degrees, the worths of the terms \$2y\$ and also \$5\$ should be in degrees. Then just the sum of them will be in degrees. So, The ax \$5\$ is created as \$5^\circ\$. Similarly, the term \$2y\$ is in degrees and also it is possible if \$2\$ is a number and also \$y\$ is an edge in degrees. Therefore, the expression \$(2y+5)^\circ\$ have the right to be created as \$2y+5^\circ\$ in the equation.

\$\implies 2y + 5^\circ + 3x = 180^\circ\$

\$\implies 3x+2y = 180^\circ -5^\circ\$

\$\therefore \,\,\,\,\,\, 3x+2y = 175^\circ\$

Case: 1

It is given that the value of \$x\$ is \$25^\circ\$, substitute it in the equation and also find the value of \$y\$ in degrees.

\$3x+2y = 175^\circ\$

\$\implies 3(25^\circ) + 2y = 175^\circ\$

\$\implies 75^\circ + 2y = 175^\circ\$

\$\implies 2y = 175^\circ -75^\circ\$

\$\implies 2y = 100^\circ\$

\$\implies y = \dfrac100^\circ2\$

\$\therefore \,\,\,\,\,\, y = 50^\circ\$

Therefore, the worth of \$y\$ is \$50\$ levels if the value of \$x\$ is \$25^\circ\$.

Case: 2

In this case, the worth of \$y = 35^\circ\$. Instead of the value of \$y\$ in the equation to achieve the worth of \$x\$ in degrees.

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\$3x+2y = 175^\circ\$

\$\implies 3x+2(35^\circ) = 175^\circ\$

\$\implies 3x+70^\circ = 175^\circ\$

\$\implies 3x = 175^\circ -70^\circ\$

\$\implies 3x = 105^\circ\$

\$\implies x = \dfrac105^\circ3\$

\$\therefore \,\,\,\,\,\, x = 35^\circ\$

Therefore, the value of \$x\$ is \$35^\circ\$ if the value of \$y\$ is same to \$35^\circ\$.