For #6-10 use the figure at the right to find each measure. In the figure, overline (UV) is a perpendicular bisector of overline (SW) ,and overline (WV) is an angle bisector of angle SWT 6. SU=underline ( ) 7 mangle VWX=underline ( ) 8 mangle WVX= __ 9 mangle XTV= __ 10. mangle XVT= __

To solve these problems, we need to use the information given in the picture details and apply geometric principles. Let's go through each step to find the measures requested.**Step 1: Find the measure of angle W (and angle T since they are equal).**Since is a perpendicular bisector of , we know that and are right angles (90 degrees each). This means that and are also right angles because they are linear pairs with and , respectively.Given that degrees and it is a right angle, we can set up the equation: Solving for x: degrees (approximately)**Step 2: Find the measure of angle XWU (and angle XUW since they are equal).**Since degrees, we can substitute the value of x we found: degrees (approximately)**Step 3: Find the measure of angle W (and angle T).**Since degrees and degrees, and is an angle bisector of , we know that .But we also know that , so we can set up the equation: Solving for y: degrees (approximately)Now we can find the measure of angle W: degrees (approximately)**Step 4: Find the measure of angle VWX.**Since , we can find by subtracting from : degrees (approximately)**Step 5: Find the measure of angle XVT.**We already have degrees, so: degrees (approximately)**Step 6: Find the measure of angle XVT (which is also ).**Since we already found in the previous step, we know that: degrees (approximately)**Step 7: Find the measure of angle XVT (which is also ).**Since we already found in the previous step, we know that: degrees (approximately)**Step 8: Find the measure of angle XVT (which is also ).**Since we already found in the previous step, we know that: degrees (approximately)**Step 9: Find the measure of angle XVT (which is also ).**Since we already found in the previous step, we know that:\[ m