(In the picture, QRST looks like a rhombus, so I will assume that it is a rhombus.)

In a rhombus, opposite angles are congruent based on the alternate interior angle theorem. In other words, R and T along with Q and S are both alternate interior angle pairs.
(You can actually test this by printing out a rhombus, cutting out the angles, and matching up the opposite ones.)

We know that Q is equal to 4x + 10, but we need to solve for x. Since Q and S are congruent, we can set them equal to each other:
1) 4x + 10 = 5x - 3
2) 4x + 13 = 5x
3) 5x = 4x + 13
4) x = 13
Now let's plug 13 in for Q:
5) 4(13) + 10 = 52+10 = 62

I got m<Q = 62 degrees. Hope this helps!

3 0

2 years ago

5. A monument casts a 78 ft. shadow at the same time that a vertical yardstick casts a 4.5 ft. shadow. How high is the monument?

rodikova [14]

Hello,

Using Thalès 's theorem:

Let's h the height of the monument.

$\dfrac{1}{h} =\dfrac{4.5}{78} \\\\h=\dfrac{78}{4.5} =\dfrac{156}{9} \approx{17.3\ (ft)}$

If you don't know what is the Thalès's theorem,

imagine that the similar triangles.

5 0

2 years ago

M DEF = 144° and m GEF = 69°. Find m DEG

kvasek [131]

Answer:

Angle DEG = 75 degrees

Step-by-step explanation:

Step 1:

m DEF - m GEF = m DEG

Step 2:

144 - 69 = 75

Answer:

75 degrees

4 0

3 years ago