Question

10. A dioganal and a side of a rhombus are of equal
length. find the measure of the angles of the rombus .​

Answer 1

here is your answerhope it is helpfulplease mark it as brainliest answer ABCD is a rhombus.⇒AC=BC ........(1)(given) BC=AB .....(2)(side of rhombus)From eqns(1) and (2)AC=BC=AB⇒△ABC is equilateral triangle.So, ∠ABC=60 ∘ ∠BCA=60 ∘ ..........(3)∠CAB=60 ∘ ..........(4)Similarly, in △ADC,AD=DC(sides of a rhombus) AD=BCBut BC=AC∴AD=AC∴AD=DC=AC∴DAC is an equilateral triangle.⇒∠CAD=60 ∘ ......(5)⇒∠ADC=60 ∘ ⇒∠DCA=60 ∘ .......(6)From eqns(3) and (6) we get∠BCA+∠DCA=60 ∘ +60 ∘ =120 ∘ ∴∠C=120 ∘ From eqns(4) and (5),∠CAB+∠CAD=60 ∘ +60 ∘ =120 ∘ ∴∠A=120 ∘ Hence the four angles of the Rhombus are 120 ∘ ,60 ∘ ,120 ∘ ,60 ∘