Question

1. The three angles of a triangle measure (2x - 10"). (x+31") and (5x + 7"). Find the value of x and hence
all the angles of the triangle
2. One of the exterior angles of a triangle is 153" and the interior opposite angles are in the ratio 5:4. Find
the three interior angles of the triangle,​

Answer 1

Answer:

1. x= 19 °

2. three interior angles are 85°, 68° and 27°

Step-by-step explanation:

1. the sum of angles of a triangle is 180°

so,

$(2x - 10) +( x + 31) + (5x + 7) = 180$

$8x + 28 = 180$

$8x = 180 - 28$

$8x = 152$

$x = 19$

2. let the two opposite interior angles be 5x and 4x

so,

as per the exterior angle property , the sum of opposite interior angles = exterior angle

therefore,

$5x + 4x = 153$

$9x = 153$

$x = 153 \div 9$

$x = 17$

so, the opposite interior angles are

5x = 5×17 = 85°

4x = 4×17 = 68°

Again as per the angle sum property , the sum of interior angles is 180 °

so,

the third angle will be

$180 - (85 + 68)$

$180 - 153$

$27$

thus the three interior angles are 85°, 68° and 27°

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