We are given a rhombus (parallelogram with four equal sides) and the relationship of the measures of one bisected angles in terms of "x".
Recall that the diagonals of a rhombus bisect the angles they join via opposed vertices, therefore the measure of these two angles given must be EQUAL to each other.
Then we can set the following equation:
10 x - 23 = 3 x + 19
and solve for "x"
subtract 3 x from both sides to gather all terms in x on the left
10 x - 3 x - 23 = 19
combine
7 x - 23 = 19
add 23 to both sides
7 x = 19 + 23
7 x = 42
divide both sides by 7 to isolate x
x = 42 / 7
x = 6
Therefore x is 6 .
and we can use its value to find the angle UTS as requested, since the addition of all four internal angles of a rhonbus must add up to 360 degrees
First calculate the angle < TUR which is the addition of the two angles we just compared:
Then, the angles 74 + 74 = 148 degrees
Now we use this information to calculate the value of angle 74 + 74 + 2 148 + 2 subtract 148 from both sides
2 2 divide by 2 both sides:
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