Question

hey guys i will feel so appreciated if u all help me in these two questions

Answer 1

angle abc+abx=180degree(linear pair)
      =:abc+110degr..=180degr..
     =abc=180-110
     =abc=70degree
hence,x=70
now we hv to find y
in triangle abc(sum of all angle measure 180 degree.
ang.(abc+bca+cab)=180degree
        =:70+y+40=180
          y=180-110
hence,y=70

Answer 2

Solutions for the Question 7 :
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AB = AC, So two sides in a traingle are equal.

Therefore, Above triangle is Isosceles triangle.
We know that, In a isosceles triangle, Base angles are equal.

So, Angle B = Angle C

Given, Angle B = 60°
So , Angle C ( Angle ACP) = 60°

In the above triangle ABP,
We have, Angle B = 60°
∠ APB = 90° ( As ∟ represents an angle of 90° )

Now, By Angle sum property.
∠B + ∠ APB + ∠BAP = 180 .
60 + 90 + ∠BAP = 180
∠BAP = 180 - 150 = 30°

$\therefore$ ∠BAP = 30° , ∠ACP ( ∠ACB) = 60°

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Solution to Question 8 :
=========================

We know that All angles on a straight line from a point equals 180°

So, ∠ABX + ∠ABC = 180°
110 + x = 180
x = 180 - 110 = 70°

So , In ΔABC,
∠B = 70°
∠A = 40°

Now, Using Angle Sum property,

∠A + ∠B + ∠C = 180°
70+40+∠C = 180
∠C = 70°

Now, In ΔABC, ∠B = ∠C

So, It is isosceles triangle. As B, C are equal. B is the base. So, Equal sides are AB, BC