Answer:
110°
Step-by-step explanation:
This quadrilateral have the same size in AD and CD, and BA and CA, so it means that, if you cut this figure in the middle (from B to D), the two triangles will be identical, and the sum of the internal angles of a triangle is 180°, so:
(110°÷2) + (30°÷2) + <C = 180°
55° + 15° + <C = 180°
70° +<C = 180°
<C = 180° - 70°
<C = 110°
And you can test it making the sum of the internal angles of the quadrilateral. The sum of the internal angles of a quadrilateral is 360°, and the angles A and C have the same measure because AD=CD and AB=BC, so:
<A + <B + <C + <D
110° + 110° + 110° + 30° = 360°
