Question

I need help i dont know what to do

Answer 1

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Answer:

  ∠CAB = 28°

  ∠DAC = 64°

Step-by-step explanation:

What you do in each case is make use of the relationships you know about angles in a triangle and around parallel lines. You can also use the relationships you know about diagonals in a rectangle, and the triangles they create.

Left

Take advantage of the fact that ∆AEB is isosceles, so the angles at A and B in that triangle are the same. If we call that angle measure x, then we have the sum of angles in that triangle is ...

  x + x + ∠AEB = 180°

  2x = 180° -124° = 56°

  x = 28°

The measure of angle CAB is 28°.

__

Right

Sides AD and BC are parallel, so diagonal AC can be considered a transversal. The two angles we're concerned with are alternate interior angles, so are congruent.

  ∠BCA = ∠DAC = 64°

The measure of angle DAC is 64°.

(Another way to look at this is that triangles BCE and DAE are congruent isosceles triangles, so corresponding angles are congruent.)