Question

question the measures of the angles of a triangle are shown in the figure below. find the measure of the smallest angle. answer attempt 1 out of 10 submit answer

Explanation:

Step1: Apply angle - sum property of triangle

$(x + 17)+(7x-16)+115 = 180$

Step2: Simplify the left - hand side

$x+17 + 7x-16+115=8x + 116$
So, $8x + 116=180$

Step3: Solve for x

$8x=180 - 116$
$8x = 64$
$x = 8$

Step4: Find the measures of the angles

Angle 1: $x + 17=8 + 17=25^{\circ}$
Angle 2: $7x-16=7\times8-16=56 - 16 = 40^{\circ}$
The third angle is $115^{\circ}$
The smallest angle is $22^{\circ}$ (since $22^{\circ}<25^{\circ}<40^{\circ}<115^{\circ}$)

Answer:

$22^{\circ}$