Question

One angle of a triangle is equal to the sum of the other two. If the ratio of the other two
angles is 7:8, find the angles of the triangle.​

Answer 1

Given :-

• One angle of a triangle is equal to the sum of the other two.  

• Ratio of the other two angles is 7:8

To Find :-

• Find the angles of the triangle.  

Solution :-

~Here, we’re given that one angle of triangle is equal to sum of other two angles ,  ratio of two angles of a triangle and we need to find measure of each angle. We can form an equation according to the given ratios and the angle sum property of a triangle. By solving that equation we can find the measure of each angle of this triangle.

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As we know that ,

★ According to the angle sum property of triangles sum of all angles of a triangle is 180°.  

Assuming angles of the triangle

• First angle = 7x + 8x = 15x  

• Second angle = 7x  

• Third angle = 8x  

Solving the equation :-

⟶ 15x + 7x + 8x = 180° 

⟶ 30x = 180°  

⟶ x = 180/30°  

⟶ x = 6°  

∴ First angle = 90°  

Second angle = 42°

Third angle = 48°  

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Hence,  

• Measure of angles of triangle are 90° , 42° and 48°

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Answer 2

Answer:

The answer is x = 11.25 I hope it was helpful.