Examkin

Question

Difficulty: EasyTriangle Properties and Angle Theorems

In △XYZ\triangle XYZ, the measure of ∠X\angle X is 50∘50^\circ, and the measure of ∠Y\angle Y is twice the measure of ∠X\angle X. What is the measure of ∠Z\angle Z?

  1. A
    80∘80^\circ
  2. B
    100∘100^\circ
  3. 30∘30^\circAnswer
  4. D
    105∘105^\circ
  5. E
    150∘150^\circ

Answer

The correct answer is 30∘30^\circ.
Since the measure of ∠X\angle X is 50∘50^\circ and the measure of ∠Y\angle Y is twice that of ∠X\angle X, the measure of ∠Y\angle Y is 2×50∘=100∘2 \times 50^\circ = 100^\circ. Because the sum of the interior angles of any triangle is 180∘180^\circ, we can find the measure of ∠Z\angle Z by subtracting the sum of the measures of ∠X\angle X and ∠Y\angle Y from 180∘180^\circ: 180∘−(50∘+100∘)=30∘180^\circ - (50^\circ + 100^\circ) = 30^\circ. Thus, the correct option is the one stating 30∘30^\circ.

Step-by-Step Solution

1
Calculate the measure of ∠Y\angle Y using the given relationship with ∠X\angle X.
∠Y=2×50∘=100∘\angle Y = 2 \times 50^\circ = 100^\circ
The problem states that the measure of ∠Y\angle Y is twice the measure of ∠X\angle X, which is given as 50∘50^\circ.
2
Calculate the measure of ∠Z\angle Z using the Triangle Angle Sum Theorem.
∠Z=180∘−(50∘+100∘)=30∘\angle Z = 180^\circ - (50^\circ + 100^\circ) = 30^\circ
The sum of the interior angles of any triangle is always 180∘180^\circ.

Key Concept

Triangle Angle Sum Theorem
Estimated Time:45s
Rate this question

Topics

Triangle Properties and Angle Theorems

More questions from this topic