Question

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4

Answer 1

m∠T = 51°

Explanation:

If two triangles are similar, their corresponding angles are the same size.

If ΔXYZ ~ ΔRST then:

• m∠X = m∠R
• m∠Y = m∠S
• m∠Z = m∠T

As m∠X = 50° and m∠S = 79° then:

• m∠X = m∠R = 50°
• m∠Y = m∠S = 79°
• m∠Z = m∠T

Interior angles of a triangle sum to 180°. Therefore:

⇒ m∠R + m∠S + m∠T = 180°

⇒ 50° + 79° + m∠T = 180°

⇒ 129° + m∠T = 180°

⇒ 129° + m∠T - 129° = 180° - 129°

⇒ m∠T = 51°

Therefore, the measure of angle T is 51°.

Answer 2

∠ T = 51°

Explanation:

since the triangles are similar then corresponding angles are congruent.

given ∠ S = 79° , then ∠ Y = 79°

the sum of the 3 angles in a triangle = 180° , so

∠ X + ∠ Y + ∠ Z = 180° , that is

50° + 79° + ∠ Z = 180°

129° + ∠ Z = 180° ( subtract 129° from both sides )

∠ Z = 51°

Then

∠ T = ∠ Z = 51°