Question

please answer my question number 10 and explain it

Answer 1

Hey Mate,

I will answer your question part-wise.

10)a) We know that the sum of all the angles in a triangle is 180°. Then,

       ∠ABC + ∠BCA + ∠CAB = 180°

       Let us take ∠ABC to be "x". Then,

            x + 60° + 50° = 180°

            x + 110° = 180°

            x = 180° - 110°

            x = 70°

Therefore, ∠ABC = 70°

10)b)

Obtuse angled triangle: A triangle that has an obtuse angle.

Acute angled triangle  : A triangle that has one or more acute angles.

Right angled triangle   : A triangle that has a right angle.

Of all these triangles, we see that ΔABC is an acute angled triangle, since, all its angles are acute angles, i.e., 50°, 60° and 70°.

Therefore, ΔABC = Acute Angled Triangle

10)c)

Equilateral Triangle : A triangle that has all three sides and angles equal.

Isoceles Triangle     : A triangle that has two of its sides and angles equal.

Scalene Triangle     : A triangle that has none of its sides or angles equal.

Of all these triangles, we see that ΔPQR is an isoceles triangle, since, two of its sides are equal, i.e., PQ and QR.

Therefore, ΔPQR = Isoceles Triangle

10)d)

Equilateral Triangle : A triangle that has all three sides and angles equal.

Isoceles Triangle     : A triangle that has two of its sides and angles equal.

Scalene Triangle     : A triangle that has none of its sides or angles equal.

Of all these triangles, we see that ΔLMN is an equilateral triangle, since, all the sides are equal.

Therefore, ΔLMN = Equilateral Triangle

10)e)

We know that an equilateral triangle has all its angles equal. So,

if we take one angle of an equilateral triangle to be "x", then,

3x = 180° ( Since, a triangle has 3 angles. )

x = 180°/3

x = 60°

Hence, the measure of one angle of an equilateral triangle is 60°

Therefore, ∠L = 60°

Hope it Helps!