Question

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3

Answer 1

m∠P = 13°, m∠Q = 65° and m∠R = 102°

Explanation:

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

If ΔCDE ~ ΔPQR then:

• m∠C = m∠P
• m∠D = m∠Q
• m∠E = m∠R

As m∠C = 13° and m∠D = 65° then:

• m∠C = m∠P = 13°
• m∠D = m∠Q = 65°
• m∠E = m∠R

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

⇒ m∠P + m∠Q + m∠R = 180°

⇒ 13° + 65° + m∠R = 180°

⇒ 78° + m∠R = 180°

⇒ 78° + m∠R - 78° = 180° - 78°

⇒ m∠R = 102°

Therefore, the measures of angles P, Q and R are:

• m∠P = 13°
• m∠Q = 65°
• m∠R = 102°

Answer 2

∠ P = 13° , ∠ Q = 65° , ∠ R = 102°

Explanation:

since the triangles are similar , then corresponding angles are congruent.

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

∠ C + ∠ D + ∠ E = 180° , that is

13° + 65° + ∠ E = 180°

78° + ∠ E = 180° ( subtract 78° from both sides )

∠ E = 102°

then

∠ P = ∠ C = 13°

∠ Q = ∠ D = 65°

∠ R = ∠ E = 102°