Question

The measures of the angles of a triangle are shown in the figure below. Find the measure of the smallest angle.

Answer 1

25°

Explanation:

sum of angles in a triangle= 180°

(x+17)° + 115°+ (7x-16)°=180°

step 2:* remove bracket and collect like terms*

that is: x+17° + 115°+ 7x-16°=180° will become

x+7x+115+17-16=180

then 8x+116 = 180

step 3: Take 116 to the other side

that is 8x = 180 -116( the sign changes when it crosses the equals to sign)

8x =64

step 4: Divide both sides by the coefficient of x

that is: 8 is the coefficient of x(meaning it carries the x sign)

8x = 64

8 8

then x = 8

step 5 : take x=8 back to the angles in the triangle

• x+17° =8 +17°=25°
• 7x-16° =7x8 -16°

=56-16=40°

• 115°

So the smallest angle is 25°

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