Find the value of X. Write your answer as a decimal.

  68.5

Step-by-step explanation:

Angles DEC and DAC are right angles, so their sum is 180°. DECA is a quadrilateral, which has a sum of interior angles equal to 360°. Then angle ACE is the supplement of angle D:

  ∠ACE = 180° -43° = 137°

Inscribed angle ABE has half the measure of central angle ACE, so we have ...

  x° = 137°/2

  x = 68.5

∠acb = 8°

step-by-step explanation:

∠xba lies on the circle and is half the measure of the intercepted arc ax

hence

measure of arc ax = 2 × 42° = 84°

∠acb is outside the circle and is

∠acb = (arcab - arcax ), hence

∠acb = 0.5 (100 - 84) = 0.5 × 16° = 8°