ABCD is a rhombus. if abc = 130 degrees, find DAC and BAC
Answers
L DAC = 25°
L BAC = 25°L BAC = 25°
Step-by-step explanation:
Given :
ABCD is a rhombus
L ABC = 130°
Since, opposite angles of a rhombus are equal.
Therefore,
L ABC = L ADC = 130°
L BAD = L BCD the
Also, diagonals of rhombus bisect each other.
→ L DAC = L BAC
To find :
L DAC and L BAC
we have,
Solution:
Sum of angles of quadrilateral is 360°
therefore,
L ABC + L BCD + L ADC + L BAD = 360°
L ABC + L BCD + L ABC + L BCD = 360°
because, L ABC = L ADC
and L BAD = L BCD
2(L ABC) + 2(L BCD) = 360°
2(L ABC + L BCD) = 360°
L ABC + L BCD = 360°/2
130° + L BCD = 180°
L BCD = 180° - 130°
L BCD = 50°. … (1)
Since,
L BCD = L BAD
From (1)
L BAD = 50°
We can write
L BAD = L DAC + L BAC
50° = L DAC + L BAC
We know that
L DAC = L BAC
therefore,
L DAC + L DAC = 50°
2(L DAC) = 50°
L DAC = 50/2 = 25°
L BAC = 25° … L DAC = L BAC