Triangles △gji and △pkh are similar, and m∠g+m∠p=50°, and m∠i=48°. what are the measures of all the angles of these triangles ?

If ΔGJI and ΔPKH are similar, then ∡G≅∡P, ∡J≅∡K and ∡I≅∡H.

We have m∡G + m∡P = 50°, therefore m∡G = m∡P = 50° : 2 = 25°.

m∡I = 48° therefore m∡H = 48°.

We know, the sum of the measures of the angles of a triangle is equal 180°.

Therefore we have the equation:

m∡G + m∡J + m∡I = 180°

25° + m∡J + 48° =180°

73° + m∡J = 180°      subtract 73° from both sides

m∡J = 107° → m∡K = 107°.

The measures of all the angles of these triangles are: and this can be determined by using the properties of the triangle.

Given :

Given that triangle GJI and triangle PKH are similar therefore:

The sum of the interior angles of the triangle is .

The measures of all the angles of these triangles are: .

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if a = 1,   and b = 2, then the answer is 47.99999999. if you round that to the nearest whole number, the answer is 48.

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