△RST ∼ △XYZ.
m∠R = 18°
, m∠S = 75°
. What are the measures of angles X
, Y
, and Z
?
m∠X =
m∠Y =
m∠Z
Since △RST ∼ △XYZ, the corresponding angles are congruent.
m∠X = 18° (corresponding to ∠R)
m∠Y = 75° (corresponding to ∠S)
m∠Z = 90° (since the sum of angles in a triangle is always 180°)
SHOW WORKKK
Sure, here's the step-by-step work to find the measures of angles X, Y, and Z:
Given:
△RST ∼ △XYZ
m∠R = 18°
m∠S = 75°
Step 1: Corresponding angles are congruent
Since △RST ∼ △XYZ, the corresponding angles are congruent. This means that ∠R and ∠X are congruent, and ∠S and ∠Y are congruent.
So, m∠X = 18° and m∠Y = 75°.
Step 2: Using the sum of angles in a triangle
The sum of the angles in a triangle is always 180°.
Let's find the measure of ∠Z.
m∠R + m∠S + m∠T = 180° (sum of angles in △RST)
Substituting the given values:
18° + 75° + m∠T = 180°
Combining like terms:
93° + m∠T = 180°
Subtracting 93° from both sides:
m∠T = 180° - 93°
m∠T = 87°
So, m∠Z = 87°.
Therefore, the final measures of angles X, Y, and Z are:
m∠X = 18°
m∠Y = 75°
m∠Z = 87°