Question

In this figure, m∠BDA = *BLANK* ° and m∠BCA =*BLANK* °.

Answer 1

well, first we need to find the angle BOA.
this is 360-250=110.
in arrow head shapes, the angle of point is half of the angle on the indent on the other side....in other words, BDA is half of BOA...=55°

BOAC is a quadrilateral so the sides add to 360°. CBO is 90° and OAC is 90°, as these angles are perpendicular to the tangent of the circle and meet at the radius.
so 360- 90-90-110=70°
hope this helps!

Answer 2

m∠BDA = 55°

m∠BCA = 70°

Explanation:

In the given figure

Tangents AC and BC

Chords AD and BD

Radius OA and OB

arc ADB (major arc AB)= 250°

minor AB + major AB = 360°

minor AB (∠AOB) = 110°

∠BDA = half of ∠AOB

(because angle makes at circle is half angle at center on same arc)

Thus, ∠BDA = 110/2 = 55°

∠OBC and ∠OAC are make 90° because radius perpendicular to tangent.

In a quadrilateral, AOBC

∠OBC + ∠OAC + ∠AOB + ∠BCA = 360°

Sum of angles of quadrilateral is 360°

90° + 90° + 110° + ∠BCA = 360°

∠BCA = 360° - 90° - 90° - 110°

∠BCA = 70°

Hence, m∠BDA = 55° and m∠BCA = 70°