Question

please help me and solve it with full explaination and solution​

Answer 1

Question :-

ABCD is the parallelogram . If ∠A = 130° , Find ∠D.

(A) 55°

(B) 50°

(C) 70°

(D) 80°

Required Answer :-

Using the properties of parallelogram ,

• Sum of the adjacent angles of a parallelogram is 180°

From the given figure ,

• ∠A and ∠D are one of the pair of adjacent angles

So ,

➙ ∠A + ∠D = 180°

We are given that ∠A = 130°

➙ 130° + ∠D = 180°

➙ ∠D = 180° - 130°

➙ ∠D = 50°

Hence ,

• The measure of ∠D is 50° and Option(B) is the required answer

Answer 2

${\large{\bold{\bf{\sf{\underline{Understanding \; the \; question}}}}}}$

➨ This question says that there is a paralloelogram named ABCD given Amd this question says that ∠A measures 130° and we have to find ∠D. And there is an attachment given to understand the question ! Options are too given below –

a. 55°

b. 50°

c. 70°

d. 80°

${\large{\bold{\bf{\sf{\underline{Given \; that}}}}}}$

➨ ∠A measures 130°

${\large{\bold{\bf{\sf{\underline{To \; find}}}}}}$

➨ Measurement of ∠D

${\large{\bold{\bf{\sf{\underline{Solution}}}}}}$

➨ ∠D measure = 50° ( Option b )

${\large{\bold{\bf{\sf{\underline{Using \; concept}}}}}}$

➨ Interior angle property of paralloelogram and it measures 180° always !

${\large{\bold{\bf{\sf{\underline{Full \; solution}}}}}}$

➨ ∠A + ∠D = 180°

➨ 130° + ∠D = 180°

➨ ∠D = 180° - 130°

➨ ∠D = 50°

• Henceforth, the measurement of ∠D is 50° ( Option b )

${\large{\bold{\bf{\sf{\underline{More \; information}}}}}}$

Parallelogram diagram -

$\setlength{\unitlength}{1 cm}\begin{picture}(0,0)\thicklines\qbezier(1,1)(1,1)(6,1)\put(0.4,0.5){\bf D}\qbezier(1,1)(1,1)(1.6,4)\put(6.2,0.5){\bf C}\qbezier(1.6,4)(1.6,4)(6.6,4)\put(1,4){\bf A}\qbezier(6,1)(6,1)(6.6,4)\put(6.9,3.8){\bf B}\end{picture}$

Parallelogram with diagonals -

$\setlength{\unitlength}{1 cm}\begin{picture}(20,15)\thicklines\qbezier(1,1)(1,1)(6,1)\qbezier(1,1)(1,1)(1.6,4)\qbezier(1.6,4)(1.6,4)(6.6,4)\qbezier(6,1)(6,1)(6.6,4)\qbezier(6.6,4)(6.6,4)(1,1)\qbezier(1.6,4)(1.6,4)(6,1)\put(0.7,0.5){\sf A}\put(6,0.5){\sf B}\put(1.4,4.3){\sf D}\put(6.6,4.3){\sf C}\end{picture}$

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Request : Please see this answer from web browser or chrome just saying because I give some diagrams here but they are not shown in app

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