please tell me the answer
Answers
a)
Given that
In ∆ABC , AB = AC
=> ∠B = ∠ C
Since, The angles opposite to equal sides are equal.
∠B = ∠ C = x°
∠A = 50°
We know that
The sum of the three interior angles in a triangle is equal to 180°.
=> ∠A + ∠B + ∠C = 180°
=> 50° + x° + x° = 180°
=> 50° + 2x° = 180°
=> 2x° = 180°-50°
=> 2x° = 130°
=> x° = 130°/2
=> x° = 65°
Therefore, x = 65°
b)
Given that
In ∆ABC , AB = AC
=> ∠B = ∠C
Since, The angles opposite to equal sides are equal.
∠B = ∠C= 65°
∠A = x°
We know that
The sum of the three interior angles in a triangle is equal to 180°.
=> ∠A + ∠B + ∠C = 180°
=> x° + 65° + 65° = 180°
=> x° + 130° = 180°
=> x° = 180°-130°
=> x° = 50°
Therefore, x = 50°
c)
Given that
In ∆ABC , AB = AC
=> ∠B = ∠ C
Since, The angles opposite to equal sides are equal.
Let ∠B = ∠ C = y°
∠A = 40°
We know that
The sum of the three interior angles in a triangle is equal to 180°.
=> ∠A + ∠B + ∠C = 180°
=> 40° + y° + y° = 180°
=> 40° + 2y° = 180°
=> 2y° = 180°-40°
=> 2y° = 140°
=> y° = 140°/2
=> y° = 70°
Therefore, ∠B = ∠ C = 70°
x is the exterior angle
We know that
The exterior angle is formed by extending any side of the triangle is equal to the sum of the two opposite interior angles.
=> x = 70°+40°
=> x = 110°
(or)
x and ∠B are linear pair
=> x + ∠B = 180°
=> x + 70° = 180°
=> x = 180°-70°
=> x = 110°
Therefore, x = 110°
Answer :-
(a) x = 65°
(b) x = 50°
(c) x = 110°
Used Properties:-
♦ The angles opposite to equal sides are equal.
♦ The sum of the three interior angles in a triangle is equal to 180°.
♦ The exterior angle is formed by extending any side of the triangle is equal to the sum of the two opposite interior angles.
Answer:
answer a) = 65°
answer b) = 57.5°
answer c) = 110°
Step-by-step explanation:
answer a) triangle ABC is an isosceles triangle
since, the base angle of isosceles triangle is always equal
therefore, angle a = angle b + angle c
= 50°= 180°
=> 130° = sum of two angle
= 130/2
=> angle x = 65°
answer b) triangle ABC is an isosceles triangle
since, the base angle of isosceles triangle is always equal
therefore, angle a = angle b + angle c
= 65°= 180°
=> 115° = sum of two angle
= 115°/2
=> angle x = 57.5°
answer c) triangle ABC is an isosceles triangle
since, the base angle of isosceles triangle is always equal
therefore, sum of two opposite interior angle of a triangle = exterior angle
=> angle x = sum of angle a and b
=> angle b = 180°-40° /2
=> angle b = 70°
=> x = 40°+70°
=> angle x = 110°