Triangle XYZ𝑋𝑌𝑍 is similar to triangle RST𝑅𝑆𝑇 such that X𝑋, Y𝑌, and Z𝑍 correspond to R𝑅, S𝑆, and T𝑇, respectively. The measure of ∠S∠𝑆 is 39°39° and 2XZ=RT2𝑋𝑍=𝑅𝑇. What is the measure of ∠Y∠𝑌?
Question
Triangle XYZ𝑋𝑌𝑍 is similar to triangle RST𝑅𝑆𝑇 such that X𝑋, Y𝑌, and Z𝑍 correspond to R𝑅, S𝑆, and T𝑇, respectively. The measure of ∠S∠𝑆 is 39°39° and 2XZ=RT2𝑋𝑍=𝑅𝑇. What is the measure of ∠Y∠𝑌?
Solution
Since the triangles XYZ and RST are similar, their corresponding angles are equal. Therefore, the measure of ∠Y is equal to the measure of ∠S. Given that the measure of ∠S is 39°, the measure of ∠Y is also 39°.
Similar Questions
For an angle with measure 𝛼 in a right triangle, 𝑠𝑖𝑛𝛼=4041 and 𝑡𝑎𝑛𝛼=409. What is the value of 𝑐𝑜𝑠𝛼?
In the figure below, 𝐴𝐵― is parallel to 𝐷𝐸―, the measure of ∠𝐴𝐵𝐶 is 49°, and the measure of ∠𝐵𝐶𝐷 is 137°. What is the measure of ∠𝐶𝐷𝐸 ?
In parallelogram ABCD below, the measure of ∠BCD is 98° and the measure of ∠CDB is 38°. What is the measure of ∠BDA ?
In the triangle below, suppose that =m∠V−4x9°, =m∠W−7x3°, and =m∠Xx°.Find the degree measure of each angle in the triangle.WVX−7x3°−4x9°x°m∠V = °m∠W = °m∠X = °
Triangle 𝐿𝑀 𝑁 is isosceles with 𝐿𝑀 = 𝐿𝑁.What is the value of 𝑦?
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.