Question

Two angles of a triangle are in the ratio 4:5 . If the sum of these angles is equal to the third angle , then find the measure of each angle of this triangle

Answer 1

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$Let\:the\:triangle(\triangle)\:be\:ABC\\\\Given,\\\\\angle A=4x\:;\:\angle B=5x\:;\:\angle C=\angle A+\angle B\\\\\implies\angle C=4x+5x=9x\\\\By\:the\:angle\:sum\:property\\\\\angle A+\angle B+\angle C=180^\circ\\\\\implies4x+5x+9x=180^\circ\\\\\implies18x=180^\circ\\\\\impliesx=\frac{180}{18}=10^\circ\\\\\therefore\angle A=4x=4\times10=40^\circ\\\\\angle B=5x=5\times10=50^\circ\\\\\angle C=9x=9\times10=90^\circ\\\\\boxed{\angle A=40^\circ\\\angle B=50^\circ\\\angle C=90^\circ}$

Answer 2

Answer:

Step-by-step explanation:

Given :-

Ratio of two angles = 4 : 5

To Find :-

The measure of each angle of this triangle.

Formula to be use :-

Angle sum property

Solution :-

Let the angles be 4x, 5x  

Then, the third angle will be 4x + 5x = 9x

⇒ 4x + 5x + 9x = 180°

⇒ 18x = 180°

⇒ x = 180/18

⇒ x = 10°

1st Angle = 4x = 10°

2nd Angle = 5x = 50°

3rd Angle = 9x = 90°

Hence, The angles are 40°, 50° and 90°.