Question

The two adjacent angles of a quadrilateral are (3x + 15)° and (x – 5)°. If the other two angles measure 75° each, Find x. 105° 120° 50° 45°

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

$\qquad\qquad\qquad\boxed{ \bf{ \: \:x = 50\degree \: \: }}$

Step-by-step explanation:

Given that, two adjacent angles of a quadrilateral are (3x + 15)° and (x – 5)°

Further given that, the other two angles measure 75° each.

We know, sum of all interior angles of a quadrilateral is 360°.

So,

$\sf \: (3x + 15)\degree + (x - 5)\degree + 75 \degree + 75\degree = 360 \degree$

$\sf \: 4x\degree + 160\degree = 360 \degree$

$\sf \: 4x\degree = 360\degree - 160 \degree$

$\sf \: 4x = 200 \degree$

$\sf\implies \bf \: x = 50 \degree$

$\rule{190pt}{2pt}$

ADDITIONAL INFORMATION

Sum of all interior angles of a convex polygon of n sides is

$\sf \:\qquad\boxed{ \sf{ \:(2n - 4) \times 90\degree \: \: }}$

For a regular polygon of n sides, we have a relationship

$\qquad\boxed{ \sf{ \:Exterior \: angle \: = \: \frac{360\degree}{n} \: }}$

$\qquad\boxed{ \sf{ \:n \: = \: \frac{360\degree}{Exterior \: angle} \: }}$

The smallest interior angle of a regular polygon is 60°.

The largest exterior angle of a regular polygon is 120°.