Question

Find the value of x & y in the following diagram. P Q R x 50 y 120

Answer 1

Answer:

Step-by-step explanation:

Find the values of the unknowns x and y in the following diagrams:

Solution 2:

(i) \angle y+\angle ACD\ =\ 180\degree\ \ \∠y+∠ACD = 180°    {linear pair}

\angle y\ +\ 120\degree\ =\ 180\degree∠y + 120° = 180°

\angle y\ =\ 60\degree∠y = 60°

By using angle sum property

In triangle ABC

\angle A+\angle B+\ \angle C\ =\ 180\degree∠A+∠B+ ∠C = 180° { \angle A\ =\ x\ ,\ \angle C\ =\ y\∠A = x , ∠C = y  }

x\ +50\degree+60\degree=\ 180\degreex +50°+60°= 180°

x\ =\ 180\degree-110\degreex = 180°−110°

x=\ 70\degreex= 70°

(ii) \angle EAD\ =\angle y\∠EAD =∠y  {vertically opposite angle are same }

80\degree=\ \angle y80°= ∠y

By using angle sum property

In triangle ABC

\angle A+\angle B+\angle C\ =\ 180\degree∠A+∠B+∠C = 180°

80\degree+\ 50\degree\ +x\ =\ 180\degree80°+ 50° +x = 180°

x\ =\ 180\degree-130\degreex = 180°−130°

x\ =\ 50\degreex = 50°

(iii) By using angle sum property

In triangle ABC

\angle A+\angle B+\angle C\ =\ 180\degree∠A+∠B+∠C = 180°

50\degree+60\degree+y\ =\ 180\degree50°+60°+y = 180°

y=\ 180\degree-110\degreey= 180°−110°

y\ =\ 70\degreey = 70°

x+y\ =\ 180\degreex+y = 180° {linear pair }

x\ +\ 70\degree=\ 180\degreex + 70°= 180°

x\ =\ 110\degreex = 110°

(iv) x\ =\ \angle DCE\x = ∠DCE  {vertically opposite angle are same }

60\degree=\ x\60°= x  

By using angle sum property

In trianfle ABC,

\angle A+\angle B+\angle C\ =\ 180\degree∠A+∠B+∠C = 180°

30\degree+60\degree+y=\ 180\degree30°+60°+y= 180°

y\ =\ 180\degree-\ 90\degreey = 180°− 90°

y\ =\ 90\degreey = 90°

(v) \angle ECD+y\ =\ 180\degree∠ECD+y = 180°

90\degree=\ y\90°= y  {vertically opposite angle are same }

In triangle ABC,

By using angle sum property,

\angle A+\angle B+\angle C\ =180\degree∠A+∠B+∠C =180°

x+x+90\degree=\ 180\degreex+x+90°= 180°

2x=180\degree-90\degree2x=180°−90°

2x=\ 90\degree2x= 90°

x\ =45\degreex =45°

(vi) by using angle sum property,

y\ =x=\ \angle A=\angle B=\angle Cy =x= ∠A=∠B=∠C {vertically opposite angle are same }

In triangle ABC

x+x+x\ =\ 180\degreex+x+x = 180°

3x=\ 180\degree3x= 180°

x=\frac{180\degree}{3}x=  

3

180°

​  

 

x\ =\ 60\degreex = 60°