Question

3. The adjacent angles of a parallelogram are (2x + 4) and (3x + 1)". Find the measures of all angles
of the parallelogramद एडजेेंट एंगल्स आफ ए पैरेललोग्राम आर टू एक्स प्लस 4 एंड थ्री एक्स प्लस 1 फाइंड द मेजर ऑफ ऑल एंगल्स ऑफ द पैरेललोग्राम ​

Answer 1

Answer:

sum of the adjacent angles of parallelogram is 180 °

hence , (2x + 4 ) + (3x + 1 ) = 180°

2x + 4 + 3x + 1 = 180°

5x + 5 = 180°

5x = 180 - 5

5x = 175

x = 175/5

x = 35

since, the angles are : 2x + 4

2(35) + 4

70+4= 74 °

another angle = 180 - 74

= 106 °

Answer 2

ANSWER:

Given:

• Adjacent angles of a parallelogram = (2x + 4)° and (3x + 1)°

To Find:

• Values of all angles of parallelogram

Diagram:

$\setlength{\unitlength}{1 cm}\begin{picture}(0,0)\thicklines\qbezier(1,1)(1,1)(6,1)\put(0.4,0.5){\bf D(2x+4)}\qbezier(1,1)(1,1)(1.6,4)\put(6.2,0.5){\bf C(3x+1)}\qbezier(1.6,4)(1.6,4)(6.6,4)\put(1,4){\bf A}\qbezier(6,1)(6,1)(6.6,4)\put(6.8,4){\bf B}\end{picture}$

Solution:

Solution:

(Refer the diagram for labelling)

We are given that,

$\implies\sf \angle ADC= (2x + 4)^{\circ}$

$\implies\sf \angle BCD= (3x + 1)^{\circ}$

We know that, the angle and its corresponding adjacent angle are supplementary ,i.e., they both add upto 180°.

So,

$\implies\sf \angle ADC + \angle BCD=180^{\circ}$

$\implies\sf (2x+4)+(3x+1)=180^{\circ}$

$\implies\sf 2x+4+3x+1=180^{\circ}$

$\implies\sf 5x+5=180^{\circ}$

$\implies\sf 5(x+1)=180^{\circ}$

$\implies\sf x+1=36^{\circ}$

So,

$\implies\sf x=35^{\circ}$

Hence,

$\:\:\bullet\:\:\bf\angle ADC=\angle ABC=(2x + 4)^{\circ}=2(35)+4=70+4=74^{\circ}$

$\:\:\bullet\:\:\bf\angle BCD=\angle BAC=(3x + 1)^{\circ}=3(35)+1=105+1=106^{\circ}$