<TVY is congruent to <Z. also, TV=6, XZ=10 and YT=8. find TX.
There must be something missing.
that is all the question says but there also is a picture
To find the value of TX, we need to use the properties of congruent angles and the given lengths of the sides.
We know that ∠TVY is congruent to ∠Z. This means that they have the same measure.
Given that TV = 6 and YT = 8, we can use the Triangle Angle-Sum Theorem to find the measure of ∠TYV. The sum of the angles in any triangle is always 180 degrees.
∠TYV + ∠TVY + ∠YTV = 180
Substituting the values we know:
∠TYV + ∠TVY + 90 = 180 (since ∠YTV is a right angle, measuring 90 degrees)
Simplifying:
∠TYV + ∠TVY = 180 - 90
∠TYV + ∠TVY = 90
Since ∠TVY and ∠Z are congruent, we can rewrite the equation as:
∠TYV + ∠Z = 90
Now, we can substitute the values:
6 + ∠Z = 90 (since TV = 6)
Simplifying:
∠Z = 90 - 6
∠Z = 84
Now, we know that ∠TYV = 90 - ∠Z.
∠TYV = 90 - 84
∠TYV = 6
Since ∠TYV and ∠TX are vertical angles (opposite angles formed by the intersection of two lines), they are congruent. Therefore, ∠TX also measures 6 degrees.
Finally, using the lengths of XZ and YT, we can find TX using the Triangle Angle-Sum Theorem again:
∠TX + ∠TYX + ∠XYZ = 180
∠TX + 6 + 90 = 180 (since ∠TYX is 6 degrees and ∠XYZ is a right angle)
Simplifying:
∠TX = 180 - 6 - 90
∠TX = 84
Therefore, TX measures 84 degrees.