Question

did you hear the story about the piece of butter?
complete each exercise. find the answer in the answer column. write the word
under the answer in the box containing the exercise letter
find the value of x.
a.
b.
c.
d.
e.
f.
g.
h.
i. a triangle contains angles measuring ( x^{circ}, 25^{circ} ), and ( 75^{circ} )
find the value of x.

Explanation:

Step1: Use the triangle - angle sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\).
For triangle A: \(x + 74+53 = 180\).

$$x=180-(74 + 53)=180 - 127=53$$

For triangle B: \(x+32 + 41=180\).

$$x=180-(32 + 41)=180 - 73 = 107$$

For triangle C: \(x+(x + 70)+28=180\).

$$2x+98 = 180$$

$$2x=180 - 98$$

$$2x=82$$

$$x = 41$$

For triangle D: \(x+47+(x - 38)=180\).

$$2x+9=180$$

$$2x=180 - 9$$

$$2x=171$$

$$x = 85.5$$

For triangle E: Using the exterior - angle property (the exterior angle of a right - triangle is equal to the sum of the non - adjacent interior angles). \(x=32 + 90=122\)
For triangle F: Using the exterior - angle property (the exterior angle of a triangle is equal to the sum of the non - adjacent interior angles). \(x=55 + 68=123\)
For triangle G: Using the exterior - angle property (the exterior angle of a triangle is equal to the sum of the non - adjacent interior angles). \(x=20 + 25=45\)
For triangle H: \(43+(x + 15)+3x=180\).

$$4x+58=180$$

$$4x=180 - 58$$

$$4x=122$$

$$x = 30.5$$

For triangle I: \(x+25 + 75=180\).

$$x=180-(25 + 75)=180 - 100=80$$

Answer:

A. \(53\), B. \(107\), C. \(41\), D. \(85.5\), E. \(122\), F. \(123\), G. \(45\), H. \(30.5\), I. \(80\)