Find the measure of

Answer:

120° , 80° , 90°

Step-by-step explanation:

The sum of the inner angles of a triangle is one hundred and eighty degrees. and as the diagram shows, The AB is equal to AC so angle ABC is equal to angle ACB so Angle A is 180°-(30°×2)=120°

you can get the second follow the above steps

and the third one is 2x+x+x=180°

so 4x=180°

so x=45°

so 2x=90°

Q.17) Given info:- In ∆ABC , AB = AC where, angle A = x°, angle B = 30°and angle C = ?°. Find the value of X in triangle ABC ?

Explanation:

Given that

ABC is a triangle

angle A = x°

angle B = 30°

angle C = ?°

And

AB =AC

We know that

In a triangle Angles opposite to equal sides are equal.

⇛Opposite angle to AB = Opposite angle to AC

⇛angle B = angle C

⇛angle B & C = 30°

We know that

The sum of all angles in a triangle is 180°

⇛ angle A + angle B + angle C = 180°

⇛30° + x° + 30° = 180°

⇛60° + x° = 180°

⇛x° = 180°÷60 = 180°:60

⇛x° = 180°/60

⇛x° = 3°

Now,

⇛angle A = x = 3°

⇛angle B = 30°

⇛angle C = 30°

Answer: The value of x for the given problem is 3°

Q.18) Given info:- In ∆ABC , AB = AC where, angle A = x°, angle B = 50°and angle C = ?°. Find the value of X in triangle ABC ?

Explanation:

Given that

ABC is a triangle

angle A = x°

angle B = 50°

angle C = ?°

And

AB =AC

We know that

In a triangle Angles opposite to equal sides are equal.

⇛Opposite angle to AB = Opposite angle to AC

⇛angle B = angle C

⇛angle B & C = 50°

We know that

The sum of all angles in a triangle is 180°

⇛ angle A + angle B + angle C = 180°

⇛ x° + 50°+50° = 180°

⇛x° + 100 = 180°

⇛x° = 180°÷100° = 180°:100°

⇛x° = 180°/100

⇛x° = 18°

Now,

⇛angle A = x = 18°

⇛angle B = 50°

⇛angle C = 50°

Answer: The value of x for the given problem is 18°

Q.19) Given info:- In ∆ABC , AB = AC and angle A = 2x°, angle B = x°, angle C = x°. Find the value of X in triangle ABC ?

Explanation:

Given that

ABC is a triangle

angle A = 2x°

angle B = x°

angle C = x°

And

AB =AC

We know that

In a triangle Angles opposite to equal sides are equal.

⇛Opposite angle to AB = Opposite angle to AC

⇛angle B = angle C

⇛angle B & C = x°

We know that

The sum of all angles in a triangle is 180°

⇛ angle A + angle B + angle C = 180°

⇛x° + 2x° + x° = 180°

⇛2x° + 2x° = 180°

⇛4x° = 180°

⇛x° = 180°÷4 = 180°:4

⇛x° = 180°/4

⇛x° = 45°

Now,

⇛angle A = 2x = 2(45) = 90°

⇛angle B = 45°

⇛angle C = 45°

Answer: The value of x for the given problem is 45°

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