Question

a 10. ABCD is a rhombus in which altitude from vertex D to side AB bsiects AB. The measures of angles of the rhombus are​

Answer 1

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Calculation :-

In ∆ ALD and ∆ BLP

DL is comman .

$\angle ALD=\angle BLD( ={{90}^{\circ }})$

$AL=BL(because D bisects AB)$

$So, ~\vartriangle ALD\cong\vartriangle BLD$ by SAS Rule.

And $AD=BD \: \: by \: \: CPCT.$

Since AD=AB ( sides of the rhombus are equal)

Therefore $AD=AB=DB=x$

So , $\vartriangle ABD$ is An Equilateral Triangle

Instructions :-

We know that each angle in an equilateral triangle is 60° . Also , Opposite Angle in rhombus are Equal and the sum of co - interior Angle is 180° .

Calculation :

Here,

$\angle A=\angle C={{60}^{\circ }}$

Also ,

$\begin{aligned}   & \text{     }\angle B+\angle C={{180}^{\circ }} \\ & \Rightarrow \angle B+{{60}^{\circ }}={{180}^{\circ }} \\ & \Rightarrow \angle B={{180}^{\circ }}-{{60}^{\circ }} \\ & \Rightarrow \angle B={{120}^{\circ }}~ \\ \end{aligned}$

So ,

$\angle D={{120}^{\circ }}~$

Then , $\angle A=\angle C={{60}^{\circ }}and \angle D=\angle B={{120}^{\circ }}~$

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