The diagram shows line m interception line in and shows some of the angle measure 120°, two times plus 10° and 2y + 30° using an angle relationship the terminal v a l u e r x in the diagram above x equals 25 BX = 50 CX = 55 DX = 60
Based on the information given, we can conclude the following:
1. The angle measure intercepted by line m and line n is 120°.
2. The angle measure intercepted by line m and line p is 2 times plus 10°. Let's call this angle measure A. Therefore, A = 2(10°) + 10° = 30°.
3. The angle measure intercepted by line m and line q is 2y + 30°.
4. The terminal value of x is given as 25.
Given that line m intercepts line n at 120° and line p at 30°, and the terminal value of x is 25, we can see that angle BXC is an exterior angle of triangle BNX. Therefore, angle BXC = angle BNX + angle NXB. Since angle BNX and angle NXB are linear pairs and thus supplementary, 120° + angle NXB = angle BXC. We know that the terminal value of x is 25, so angle NXB = x° = 25°. Therefore, angle BXC = 120° + 25° = 145°.
Now let's consider triangle DCX. We know that angle BXC = 145°, so angle DXC = 180° - angle BXC = 180° - 145° = 35°. Since angle DXC = 35°, we can conclude that angle DCX = angle DXC = 35°.
Given that angle DCX = angle DXC = 35°, and we know that angle CXB and angle BXC are linear pairs and thus supplementary, we can calculate angle CXB. We know that angle BXC = 145°, so angle CXB = 180° - angle BXC = 180° - 145° = 35°. Therefore, angle CXB = 35°.
Now that we have the angle measures of triangle DCX, we can calculate the remaining angles. In triangle DCX, we have angle DCX = angle DXC = 35° and angle CXD = 90° (as it is a right angle). Since the sum of the angles in a triangle is 180°, we have:
angle DCX + angle DXC + angle CXD = 180°
35° + 35° + 90° = 180°
This gives us 160° = 180°, so the sum of the angles in triangle DCX is not consistent with the properties of a triangle. Therefore, the given values for BX, CX, and DX are not accurate.
In conclusion, based on the given information, we can determine that angle BXC is 145° and angles DCX, DXC, and CXB are each 35°. However, the values given for BX, CX, and DX are not accurate.