Question

Please help with geometry question

Answer 1

Answer:

m∠J = 45° , m∠I = 45° and m∠M = 90°

And the ΔJIM is an isosceles right angled triangle.

Step-by-step explanation:

(a). In ΔJIM,

∠J = 2x + 15,

∠I = 5x - 30, and

∠M = 6x

Now, using angle sum property of a triangle that sum of all the angles in a triangle is 180°

⇒ ∠J + ∠I + ∠M = 180°

⇒ 2x + 15 + 5x - 30 + 6x = 180°

⇒ 13x -15 = 180°

⇒ 13x = 195

⇒ x = 15

Therefore, m∠J = 45° , ∠I = 45° and m ∠M = 90°

(b). Now, ΔJIM is a right angled triangle right angled at M.

Also, ∠J = ∠I = 45°

So, JM = IM ( because in a triangle sides opposite to equal angles are equal)

So, ΔJIM is an isosceles triangle because its two sides are equal.

Hence, ΔJIM is a right angled isosceles triangle right angled at M.