Question

The diagonals AC and BD of rectangle ABCD intersect at point O. If m∠CAB = 25°, find m∠DAC and m∠ACD.

Answer 1

In rectangle ABCD, m$\angle$CAB = 25°
$\angle$CAB + $\angle$DAC = 90° (All the angles formed by the sides of a rectangle are equal to 90°)
$\angle$DAC = 90° – 25° = 65°
m$\angle$DAC = 65°
Now in ∆ADC, $\angle$ADC + $\angle$ACD + $\angle$DAC = 180° (Sum of all the angles of a triangle is 180°)
m$\angle$ACD = $\angle$ACD = 180° – ($\angle$ADC + $\angle$DAC)
= 180° – (65° + 90°) = 25°
∴ m$\angle$DAC = 65°
m$\angle$ACD = 25°