Question

in a rhombus ABCD angle ACB is equal to 60 find (a) angle bac (b) angle dca (c) angle adc

Answer 1

Given:- ∠ACB=60°
So, ∠ACB=∠BAC=60° [ angles opposite to equal side are equal ]

In triangle BAC:-

∠ACB+∠BAC+∠CBA=180° [ ANGLE SUM PROPERTY OF A TRAINGLE ]
60°+60°+∠CBA=180°
120°+∠CBA=180°
∠CBA=180°-120°
∠CBA=60°

We know that rhombus is a parallelogram, and opposite angles of a parallelogram are equal.

So,∠CBA=∠ADC=60° [ OPPOSITE ANGLES OF A PARALLELOGRAM ARE EQUAL AND RHOMBUS IS ALSO A PARALLELOGRAM ]

∠ACB=∠DAC=60° [ ALTERNATE INTERIOR ANGLES ARE EQUAL ]

In triangle ADC:-

∠ADC+∠DAC+∠DCA=180° [ ANGLE SUM PROPERTY OF A TRIANGLE ]

60°+60°+∠DCA=180°
120°+∠DCA=180°
∠DCA=180°-120°
∠DCA=60°

So, ∠DCA=60°

∠BAC=60°

∠ADC=60°

Answer 2

Answer:

Step-by-step explanation: