Question

The sum of interior opposite angles of a quadrilateral is 130 degree and the third angle is 90 degree. find the measure of fourth angle and the adjacent exterior angle of a right angle.​

Answer 1

Given :

The sum of interior opposite angles of a quadrilateral = 130°

The measure of third angle = 90°

To Find :

(A) The measure of fourth angle

(B) The adjacent exterior angle of a right angle.

Solution :

As The measure of four angles of quadrilateral = 360°

(A)

Let the forth angle = x°

ABCD is a quadrilateral

∵ The sum of interior opposite angles of a quadrilateral = 130°

i.e  ∠B + ∠D = 130°

And

Let The third angle = ∠C = 90°

∴  ∠A + ∠B + ∠C + ∠D = 360°

Or, x + ( 130°) + 90° = 360°

Or,  x + 220° = 360°

Or,   x =  360° -  220°

i.e    x = 140°

So, The measure of fourth angles of quadrilateral = x = 140°

(B)

As The number of sides of a quadrilateral = 4

And

we know that sum of exterior angles of a polygon = 360°            

∴ 4 exterior angles = 360°          

Or, 1 exterior angle = $\dfrac{360}{4}$ = 90°

i.e The adjacent exterior angle of a right angle = 90°

Hence,

(A) The measure of fourth angles of quadrilateral is 140°

(B)  The adjacent exterior angle of a right angle is 90°  . Answer