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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 ?

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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°.

Answer: ΔGJI and ΔPKH: 25°, 107°, 48°

The measures of all the angles of these triangles are: [tex]\rm 25^\circ,\;48^\circ\;and \; 107^\circ[/tex] and this can be determined by using the properties of the triangle.

Given :

  • Triangles △GJI and △PKH are similar.
  • m∠G + m∠P = 50°, and m∠I = 48°.

Given that triangle GJI and triangle PKH are similar therefore:

[tex]\rm \angle G = \angle P[/tex]

[tex]\rm \angle J = \angle K[/tex]

[tex]\rm \angle I = \angle H[/tex]

The sum of the interior angles of the triangle is [tex]180^\circ[/tex].

[tex]\rm \angle G + \angle I + \angle J = 180^\circ[/tex]

[tex]\rm 25^\circ + 48^\circ + \angle J = 180^\circ[/tex]

[tex]\rm 73^\circ + \angle J = 180^\circ[/tex]

[tex]\rm \angle J = 107^\circ = \angle K[/tex]

The measures of all the angles of these triangles are: [tex]\rm 25^\circ,\;48^\circ\;and \; 107^\circ[/tex].

For more information, refer to the link given below:

https://brainly.com/question/10652623

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