Question

In a quadrilateral ABCD, ∠A = 72° and ∠C is the supplementary of ∠A. The other two angles are 2x–10 and x + 4. Find the value of x and the measure of all the angles.

Answer 1

Solution :

Given ABCD is a Quadrilateral.

<A = 72° ,

<C = ( 180 - 72 ) [ given ]

<C = 108°

<B = 2x - 10 ,

<D = x + 4 ,

We know that ,

<A + <B + <C + <D = 360°

<A + <C = 180°

[ supplementary angles ]

Therefore ,

<B + <C = 180°

=>2x - 10 + x + 4 = 180°

=> 3x - 6 = 180°

=> 3x = 186

=> x = 186/3

x = 62

Therefore ,

<A = 72° ,

<C = 108° ,

<B = 2x - 10 = 2×62 -10

= 124 - 10

= 114°

<C = x + 4

= 62 + 4

= 66°

••••

Answer 2

Step-by-step explanation:

substitute x in 2x+10

2*62 +10

62+4

hope this helps