Question

In the adjoining figure, ABCD is a rhombus in which angle BAC = 40°.
Find the measures of:
(i) angle ACB (ii) angle ABC (iii) angle ADC (iv) angle ACD (v)angle CAD​

Answer 1

$\mathbf{\huge{\underline{\underline{ \pink{Figure :- }}}}}$

$\setlength{\unitlength}{1.5cm}\begin{picture}(8,2)\thicklines\put(8.6,3){\large{D}}\put(7.7,0.9){\large{A}}\put(11.1,0.9){\large{B}}\put(8,1){\line(1,0){3}}\qbezier(11,1)(11.5,2)(12,3)\put(9,3){\line(3,0){3}}\put(8,1){\line(2,1){4}}\qbezier(8,1)(8.5,2)(9,3)\put(12.1,3){\large{C}}\qbezier(8.6,1.3)(8.96,1.4)(8.9,1)\put(9,1.2){\sf 40^{\circ} }\end{picture}$

⠀⠀

$\mathbf{\huge{\underline{\underline{ \red{Question ?}}}}}$

➣ In the adjoining figure, ABCD is a rhombus in which angle BAC = 40°.Find the measures of:(i) ∠ACB (ii) ∠ABC (iii) ∠ADC (iv) ∠ACD (v) ∠CAD

$\huge \bf{ \underline{\underline{\orange{Answer : - }}}}$

➢ ∠ACC = 40°

➢ ∠ABC = 100°

➢ ∠ADC = 100°

➢ ∠ACD = 40°

➢ ∠CDA = 40°

$\huge {\bf{\underline{\underline{\green{Given :- }}}}}$

➛ ∠BAC = 40°

$\huge \bf{ \underline{ \underline{ \blue{To\:Find:- }}}}$

➛ ∠BAC = ?

➛ ∠ABC = ?

➛ ∠ADC = ?

➛ ∠ACD = ?

➛ ∠CAD = ?

⠀⠀

❏ Aᴄᴄᴏʀᴅɪɴɢ ᴛᴏ ɢɪᴠᴇɴ ϙᴜᴇsᴛɪᴏɴ

⠀⠀

i) ∠BAC = 40°

Since, AB = BC

⟾ ∠ACB = ∠BAC = 40°

⠀ ∴ ∠ACB = 40°

⠀⠀

ii) In △ABC

∠ABC + ∠BAC + ∠BCA = 180°

⟾ ∠ABC = 180° - 80°

⠀ ∴ ∠ABC = 100°

⠀⠀

iii) Now ∠ADC = ∠ABC

[∵ In Rhombus opposite angle are equal]

⠀ ∴ ∠ADC = 100°

⠀⠀

iv) Since, AD = AC

∠ACD = ∠CAD = $\large{\sf{\frac{180 \degree - 100 \degree}{2}}}$

⟾ $\large{\sf{\frac{\cancel{80 \degree}}{\cancel{2}}}}$ = 40°

⠀ ∴ ∠ACD = 40°

⠀⠀

v) ∠CAD = 40°

Answer 2

Answer:

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