Question

ABCD is a rhombus.If angleDAC=50°,find (a)angleACD(b)angleCAB(c)angleABC

Answer 1

Hola Mate !!

Here's your answer :-

ang. ABC = ang. ADC { ▪ opposite angles of a rhombus are equal }
=>ang. ABC = 50°

AB || CD , AC is a transversal.
So, ang. ACD = ang. CAB { ▪ alternate interior angles are equal }........ ( 1 )

Now,
Triangle ADC is an isosceles triangle, where AD = AC ( sides of rhombus are equal ) & ang. A = ang. B ( angles opposite to the equal sides are equal )

/_DAC + /_DCA + /_ADC =180° { ▪ sum of interior angles ofa triangle }
=>2/_ACD + 50° = 180° { ▪ ang. ACD = DAC = DCA }
=>2/_ACD = 180° - 50°
=>/_ACD = 130°/2
=>/_ACD = 65°

ang. CAB = ang. ACD ( from ( 1 ))
=>ang. CAB = 65°

HOPE YOU UNDERSTAND