WEBVTT 00:00:00.700 --> 00:00:07.930 In the figure, line segments 𝐴𝐸 and 𝐡𝐢 pass through the center of the circles. 00:00:08.540 --> 00:00:21.000 Given that the measure of angle 𝐹𝐸𝐷 equals 50 degrees and the measure of angle 𝐢𝐡𝐴 is equal to two π‘₯ minus 10 degrees, find π‘₯. 00:00:21.630 --> 00:00:39.220 We are told in the question that line segments 𝐴𝐸 and 𝐡𝐢 pass through the center of the circles and that the measure of angles 𝐹𝐸𝐷 and 𝐢𝐡𝐴 are 50 degrees and two π‘₯ minus 10 degrees, respectively. 00:00:40.110 --> 00:00:44.930 We begin by recalling that angles subtended from the same arc are equal. 00:00:45.620 --> 00:00:50.730 And we also know that angles subtended from arcs with equal measure are equal. 00:00:51.400 --> 00:01:04.840 This is really useful when we’re working with a pair of concentric circles as in this question, as we’re able to say that the measure of arc 𝐹𝐷 is equal to the measure of arc 𝐢𝐴. 00:01:05.530 --> 00:01:09.740 And they are both equal to the measure of the central angle shown. 00:01:10.460 --> 00:01:18.010 Since the measure of those two arcs are equal, then the measure of any angle subtended from the arcs must also be equal. 00:01:18.710 --> 00:01:25.880 In other words, the measure of angle 𝐹𝐸𝐷 must be equal to the measure of angle 𝐢𝐡𝐴. 00:01:26.590 --> 00:01:32.010 This means that 50 degrees is equal to two π‘₯ minus 10 degrees. 00:01:32.600 --> 00:01:36.920 And 50 must be equal to two π‘₯ minus 10. 00:01:37.640 --> 00:01:43.330 We can now solve this equation for π‘₯ by firstly adding 10 to both sides. 00:01:43.910 --> 00:01:47.650 This gives us 60 is equal to two π‘₯. 00:01:48.500 --> 00:01:56.680 We can then divide through by two such that 30 is equal to π‘₯ or π‘₯ is equal to 30.