Question

hi can someone please help me with this question? thanks! :)

Answer 1

Answer:

116°

Step-by-step explanation:

Based on the figure, it is a parallelogram. Also, lines QT and RS have the same length. So we can conclude that angles Q and R are congruent (as are angles T and S).

Solve for x:

$(9x-17)=(4x+28)$

Simplify parentheses:

$9x-17=4x+28$

Add 17 to both sides:

$9x-17+17=4x+28+17\\9x=4x+45$

Subtract 4x from both sides:

$9x-4x=4x-4x+45\\5x=45$

Divide 5 from both sides:

$\frac{5x}{5} =\frac{45}{5}\\ \\x=9$

Now that we know the value of x, insert it's value into the expressions:

$(9(9)-17)\\(4(9)+28)$

Simplify parentheses:

$(81-17)\\(36+28)$

Simplify:

$(64)\\(64)$

The angles Q and R are 64°. Now that we know this, we can find the angle measure of T. The degree measure of a trapezoid add up to 360°, so add the angles of Q and R:

$64+64=128$

Subtract the total of two angles from 360°:

$360-128=232$

Divide 232° between the two remaining angles:

$\frac{232}{2}=116$

The angle measure of T is 116°.

Finito.