Answer:
Therefore angle measure are
[tex]x=50\°\\y=70\°\\z=60\°\\w=70\°[/tex]
Step-by-step explanation:
Given:
△ABC ∼ △A1B1C1.
∠A = 60°
∠B1 = 50°
∠B =x , ∠C = y , ∠A1 = z , ∠C1 = w
To Find:
angle measures,
x = ?, y = ? ,z = ?, w = ?
Solution:
△ABC ∼ △A1B1C1. .............Given:
If two triangles are similar then the corresponding angles of similar triangles are congruent.
∴ ∠A ≅ ∠A1 .............1
∠B ≅ ∠B1 .............2
∠C ≅ ∠C1 .............3
But ,∠A = 60° ,∠B1 = 50° given
∴ ∠A ≅ ∠A1 = 60° ................Transitive Property
∠B ≅ ∠B1 = 50° ................Transitive Property
Therefore
∠B =x = 50°, ∠A1 = z = 60° ,
Now,
In a Triangle sum of the measures of all the angles of a triangle is 180°.
In ΔABC we have
[tex]\angle A+\angle B+\angle C=180[/tex]
Substituting the given value we get
[tex]60+50+y=180\\y=180-110=70\\y=70\°[/tex]
m∠C = y = 70°
But ∠C ≅ ∠C1 ............From 3
∴ ∠C1 = w = 70° ................Transitive Property
Therefore angle measure are
[tex]x=50\°\\y=70\°\\z=60\°\\w=70\°[/tex]
