Can you find the angle X?

Added: 2026-05-26

[00:00:00]Can you find the angle X given A is an angle bis sector.

[00:00:14]A is an angle bis sector.

[00:00:24]That means these two angles will be equal. Suppose alpha and now BC is 14 and suppose BP is A then CP will be 14 minus A and in any triangle A B C.

[00:01:04]If A is angle bis sector then AB over A C is equal to BP over CP.

[00:01:26]And here a is angle bis sector.

[00:01:38]So a b over a c it will be bp over cp and a b is 30 over a c is 40 and bp is a over cp is 14 minus A and zero will get cancelled.

[00:02:18]for 3 over 4 is a over 14 - a and if we cross multiply then 3 * 14 - a it will be 4 * a and 42 - 3 a is 4 a.

[00:02:45]So 42 it is 4 a + 3 a and 42 is 7 a. So a will be 42 divided by 7 that will be six.

[00:03:12]So a is 6 that means 14 minus a will be 8.

[00:03:24]and now AC is 40.

[00:03:50]And from point P.

[00:04:00]If we make PQ such that angle APQ is X angle AQ is X.

[00:04:17]It is our construction.

[00:04:25]Then interangle AB and triangle AQ.

[00:04:42]Angle P A B is equal to angle P A Q that is alpha.

[00:04:54]A is common and angle A B is equal to angle A Q that is X.

[00:05:13]So triangle AB is congruent to triangle AQ.

[00:05:26]Hence AB it will be equal to AQ and AB is 30.

[00:05:43]That means a Q it will be also 30 and BP it will be equal to QP and BP is six. That means QP is also six and now CQ is AC c minus AQ and AC c is 40 minus AQ is 30 that will be 10.

[00:06:36]CQ is 10 and interangle CPQ.

[00:06:52]It is C P Q PQ is 6. CP is 8.

[00:07:01]and cq is 10. And we know that 6 a² + 8² is 10².

[00:07:13]That means angle cpq is 90°.

[00:07:23]This angle is 90°.

[00:07:29]And now at point P this angle is 90°.

[00:07:41]This angle is X. This angle is X.

[00:07:46]So X + X plus 90° is 180°.

[00:07:55]That means x will be 45°.