The Answer is: x = 29
Put all of the angles equal to 360 degrees:
(5x - 8) + (3x + 4) + 89 + 51 = 360
Collect like terms and solve for x:
5x + 3x - 8 + 4 + 89 + 51 = 360
8x - 4 + 140 = 360
8x + 136 = 360
8x = 224
x = 224/8 = 28
*** Corrected 12/272019 *** Thanks to the Moderator!
sorry i needed some points its the same answer
A quadrilateral is a polygon which has 4 vertices and 4 sides enclosing 4 angles and the sum of all the angles is 360°. When we draw a draw the diagonals to the quadrilateral, it forms two triangles. Both these triangles have an angle sum of 180°. Therefore, the total angle sum of the quadrilateral is 360°.
1) If all angles of a quadrilateral are right angles, then the quadrilateral must be a square. This is not true because the quadrilateral can also be a rectangle.
2) Two shapes are similar if and only if their corresponding angles are equal. This is true.
3) All quadrilaterals have four sides, and the sum of all angles in a quadrilateral is 180º. This is false because the sum of the angles is 360°
4) if the diagonals of a quadrilateral are perpendicular bisectors, then the quadrilateral must be a rhombus. This is true.
5) There are three vertices in a triangle, or there are four sides in a pentagon. This is false because a Pentagon has 5 sides.
6) Any two triangles are either similar or congruent. This is not true. Congruent triangles are always similar
Therefore, the true statements are 2 and 4
The statement which is true is, If the diagonals of a quadrilateral are perpendicular bisectors, then the quadrilateral must be a rhombus.
In a rhombus, the diagonals bisect at perpendicular angles to form 4 triangles.Because the diagonals bisect at right angles, then it is possible to prove that the four small formed triangles are similar using the SAS theorem: two triangles are equal if two sides are equal and the angles between the two sides are equal.In your case, the sides are that on the base and that forming a height of the triangles with both having angle 90° between the sides.So you see if these the two are congruent, the hypotenuse of these triangles are congruent, making this quadrilateral a rhombus.
Keywords : quadrilateral, rhombus, perpendicular bisector, angles
the sum of interior angles in a quadrilateral is equal to three hundred sixty....