∠SRT≅∠STR, m∠SRT = 40, m∠STU = 4x Find the value of x. The diagram is not to scale

Answer 1

Since ∠SRT ≅ ∠STR, we know that these angles are congruent. Therefore, m∠SRT = m∠STR. Since m∠SRT is given as 40, we can conclude that m∠STR = 40 as well.

Also, since ∠SRT and ∠STR are vertical angles, they are congruent to ∠STU. Therefore, we have ∠STU ≅ ∠SRT ≅ ∠STR.

Since the sum of the angles in a triangle is 180 degrees, we can write the equation:

∠SRT + ∠STR + ∠STU = 180

Substituting the known values, we have:

40 + 40 + 4x = 180

Simplifying, we get:

80 + 4x = 180

Subtracting 80 from both sides, we have:

4x = 100

Dividing both sides by 4, we find:

x = 25

Therefore, the value of x is 25.