Angles of a Triangle | Triangle Sum Theorem | MathHelp.com - By MathHelp.com
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| 00:00 | in this problem we are given a triangle and information | |
| 00:04 | about each of its angles and we're asked to find | |
| 00:08 | the value of X . And the measure of each | |
| 00:11 | missing angle in the triangle . Remember from the previous | |
| 00:15 | example that the measures of the angles of a triangle | |
| 00:19 | always add to 180°. . So we can set up | |
| 00:25 | the equation 12 x plus eight plus 55 Plus eight | |
| 00:35 | x -3 equals 180 . and simplifying on the left | |
| 00:41 | side , we have 20 x plus 60 Equals 180 | |
| 00:50 | And subtracting 60 from both sides . Yes , yeah | |
| 00:55 | , Gives us 20 x equals 120 And dividing both | |
| 01:02 | sides by 20 . We find that X equals six | |
| 01:09 | . Yeah . Now , to find the measures of | |
| 01:13 | each of the missing angles in the triangle , remember | |
| 01:17 | that the measure of angle P is 12 X plus | |
| 01:21 | eight . So if we plug a six in for | |
| 01:24 | X then we have for the measure of angle p | |
| 01:31 | 12 times six plus 8 Which is 72 plus eight | |
| 01:40 | or 80 degrees . So the measure of Angle P | |
| 01:46 | is 80°. . And remember that the measure of angle | |
| 01:51 | are is eight X -3 . So if we plug | |
| 01:55 | a six in for X , then for the measure | |
| 01:58 | of angle are yes , yes , We have eight | |
| 02:03 | times 6 -3 , Which is 48 -3 or 45 | |
| 02:13 | degrees . So the measure of angle are Is 45°. | |
| 02:21 | . Finally we can check our answer by making sure | |
| 02:25 | that the three angles of the triangle add to 180°. | |
| 02:31 | . 55 plus 80 is 135 Plus 45 is 180 | |
| 02:40 | . So our answer checks . |
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