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 A:

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

For B:

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

For C:

\(x+(x + 70)+28=180\)
\(2x+98 = 180\)
\(2x=180 - 98\)
\(2x=82\)
\(x = 41\)

For D:

\(x+(x - 38)+42=180\)
\(2x + 4=180\)
\(2x=180 - 4\)
\(2x=176\)
\(x = 88\)

For E:

The exterior angle property: The exterior angle of a right - triangle is equal to the sum of the non - adjacent interior angles.
\(x=32 + 90\)
\(x = 122\)

For F:

The exterior angle property: \(x=68 + 56\)
\(x = 124\)

For G:

The sum of the interior angles of a triangle is \(180^{\circ}\). The angle adjacent to \(x\) (using the exterior - angle property for the non - drawn part):
Let's assume the non - drawn angle in the triangle with \(20^{\circ}\) and \(25^{\circ}\) is \(y\), \(y=180-(20 + 25)=135^{\circ}\). Then \(x = 180 - 135=45\)

For H:

The sum of the interior angle and the exterior angle:
The interior angle adjacent to \(3x\) is \(180 - 3x\). Then \(x+(x + 15)+(180 - 3x)+43=180\)
\(x+x + 15+180-3x + 43=180\)
\(-x+238 = 180\)
\(-x=180 - 238\)
\(-x=-58\)
\(x = 58\)

For I:

Using the triangle - angle sum theorem \(x+25 + 75=180\)
\(x+100 = 180\)
\(x=80\)

Answer:

A. \(53\) (not in the right - hand column), B. \(107\) (MIND), C. \(41\) (I), D. \(88\) (not in the right - hand column), E. \(122\) (WANT), F. \(124\) (TO), G. \(45\) (SPREAD), H. \(58\) (DON'T), I. \(80\) (AROUND)