Question

Find the value of x if the angles of a quadrilateral are (3x - 5)° , (8x - 15)°, (2x + 4)° and 90° . Also find the measure of x.

Answer 1

Total sum of quadrilateral =360
Angles given are(3x-5),(8x-15),(2x+4),90
3x-5 +8x-15+2x+4+90=360
13x-74=360
13x=360-74
13x=286
X= 286/13
=22
Angles are(3*22-5)
=61
(8*22-15)=161
(2*22+ 4)=48

Answer 2

Given,

• The angles of a quadrilateral are (3x - 5)°, (8x - 15)°, (2x + 4)° and 90°.

To find,

• The measure of x.

Solution,

We can simply find the value of x by using the angle sum property which states that the sum of all four interior angles of a quadrilateral is equal to 360°

Let us suppose ABCD be a quadrilateral in which ∠ A = (3x - 5)°, ∠B = (8x - 15)°, ∠C = (2x + 4)°, and ∠D = 90°.

Then, by angle sum property,

∠A + ∠B+ ∠C+ ∠D = 360°

3x-5 + 8x-15 +2x+4 +90° = 360°

       3x-5 + 8x-15 +2x+4  = 360 -90

       3x +8x+2x -5-15+4   = 270

                         13x  -16    = 270

                                 13x   = 270 +16

                                  13x  = 286

                                     x  = 286/13

                                     x  = 22

Then, ∠ A =  (3x - 5)°

                 = 3(22) -5

                 = 66 -5

          ∠ A = 61°

          ∠ B = (8x - 15)°

                 = 8(22) -15

                = 176 -15

      ∠ B    = 161°

         ∠ C =  (2x + 4)°

                = 2(22) +4

                = 44 +4

      ∠ C    = 48°

      ∠ D    = 90°

Hence, the value of x if the angles of a quadrilateral are (3x - 5)°, (8x - 15)°, (2x + 4)° and 90° is 22 and the measure of the angles are 61°, 161°, 90°, and 48°.