Question

The angles of a quadrilateral are (6x-10), (4x+20), (3x + 25)° and (7x - 15)". Find the
measure of all the angles.

Answer 1

Answer:

The angles are : 92°, 88°, 76°, and 104°

Explanation :

Given angles :

${(6x - 10)\degree, \: (4x + 20)\degree, \: (3x + 25)\degree, \: (7x - 15)\degree}$

We know that,

The sum of all angles in a quadrilateral equals to 360°.

According to the question,

${ \implies (6x - 10)\degree + \: (4x + 20)\degree + \: (3x + 25)\degree + \: (7x - 15)\degree = 360 \degree}$

Solving for $\pmb{x :}$

${ \implies (6x - 10)\degree + \: (4x + 20)\degree + \: (3x + 25)\degree + \: (7x - 15)\degree = 360 \degree}$

$\implies 6x - 10 + 4x + 20 + 3x + 25 + 7x - 15 = 360 \degree$

$\implies 6x + 4x + 3x + 7x - 10 + 20 + 25 - 15 = 360\degree$

$\implies 20x + 20 = 360 \degree$

$\implies 20x = (360 - 20) \degree$

$\implies 20x = 340 \degree$

$\implies x = \frac{340}{20}$

$\implies x = 17 \degree$

$\therefore \sf \: The \: value \: of \: \boldsymbol{x} \: is \: 17 \degree$

Hence, the angles are :

• $(6x - 10)\degree = \bf 6(17) - 10 = 92 \degree$
• $(4x + 20)\degree = \bf 4(17) + 20 = 88 \degree$
• $(3x + 25)\degree \bf = 3(17) + 25 = 76 \degree$
• $(7x - 15)\degree = \bf 7(17) - 15 = 104 \degree$

_____________________

Angle sum property :

• The sum of all angles in a quadrilateral is 360° and this is known as the angle sum property of a quadrilateral.

Answer 2

$\large \frak \green{ \pmb{ \underline{Given :}}}$

• The angles of a quadrilateral are (6x-10), (4x+20), (3x + 25)° and (7x - 15).

$\large \frak \green{ \pmb{ \underline{To \: find :}}}$

• Find the measure of all angles.

$\large \frak \green{ \pmb{ \underline{Solution :}}}$

$\sf{We \: know \: that,}$

$\boxed{ \sf \pink{ \underline{Sum \: of \: all \: angles \: of \: quadrilateral \: is \: 360⁰.}}}$

$\sf{ \therefore \: (6x-10) + (4x+20) + (3x + 25) + (7x - 15) = {360}^{0} }</p><p>$

$\sf{ \qquad : \implies \: 6x + 4x + 3x + 7x-10 +20 + 25 - 15 = {360}^{0} }</p><p>$

$\sf{ \qquad : \implies \: 20x + 20 = {360}^{0} }$

$\sf{ \qquad : \implies \: 20x = 360 - 20}$

$\sf{ \qquad : \implies \: 20x = 340}$

$\sf{ \qquad : \implies \: x = \frac{340}{20} }$

$\boxed{\sf \red{ \qquad : \: \implies \: x = 17}}$

______________________________________

⠀

⠀

$\sf{1) \: (6x - 10 )= 6 \times 17 - 10 = \orange{ {92}^{0} }}$

$\sf{2) \: (4x + 20) = 4 \times 17 + 20 = \color{greenyellow}{ {88}^{0} }}$

$\sf{3) \: (3x + 25) = 3 \times 17 + 25 = \color{skyblue} {{76}^{0} }}$

$\sf{4) \: (7x - 15) = 7 \times 17 - 15 = \color{pink}{ {104}^{0} }}$

⠀

⠀

⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━⠀⠀