One angle of a triangle is twice as large as another. The third contains 5 degrees more than the larger of these. Find the smallest angle

Answer 1

One angle of a triangle is twice as large as another. The third contains 5 degrees more than the larger of these. Find the smallest angle

......Okay given the sum triangle theorem....stated below from wikipedia.....

In a Euclidean space, the sum of angles of a triangle equals the straight angle (180 degrees, π radians, two right angles, or a half-turn). A triangle has three angles, one at each vertex, bounded by a pair of adjacent sides.

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One angle of a triangle is twice as large as another. The third contains 5 degrees more than the larger of these. Find the smallest angle

Let X be the first angle.......and Y be the second angle......and Z be the third angle......

X+Y+Z = 180 degrees

X = 2Y

Z = X + 5

.......the smallest angle is Y.......You now have 3 equations and 3 unknowns.......

....using substitution.....we have....

X + 1/2(X) + X+5 = 180.......NOW solve for X

2X + X + 2X + 10 = 360......Multiply both sides by 2.....removes the fraction for easy computing....

5X + 10 = 360.........subtract both sides by 10......

5X = 350

+

X = 70

NOW LETS CHECK.......IF X = 70...THEN Y=1/2(70)=35 Z = X + 5 = 70 + 5 = 75......

Is X + Y + Z = 180.......70 + 35 + 75 = 180.....that checks......so Y your smallest angle is 35