Question

no school details were added for this assignment. it is given that ∠wxy and ∠yxz are blank. ( mangle wxy + mangle yxz = 180^circ ) using the blank. it is also given that ( mangle wxy = 75^circ ). using the substitution property of equality, ( 75^circ + mangle yxz = 180^circ ). therefore, using the subtraction property of equality, ( mangle yxz = ) blank.
options (left boxes): complementary angles, supplementary angles, definition of supplementary angles, definition of complementary angles, ( 75^circ ), ( 105^circ ), ( 180^circ )

Explanation:

Step1: Identify the relationship

We know that \( m\angle WXY + m\angle YXZ = 180^\circ \) (given, and this is the definition of supplementary angles, as supplementary angles sum to \( 180^\circ \)).

Step2: Substitute the known value

We are given \( m\angle WXY = 75^\circ \). Substituting this into the equation \( 75^\circ + m\angle YXZ = 180^\circ \).

Step3: Solve for \( m\angle YXZ \)

Using the subtraction property of equality, subtract \( 75^\circ \) from both sides: \( m\angle YXZ = 180^\circ - 75^\circ \).
Calculating the right - hand side: \( 180 - 75=105 \), so \( m\angle YXZ = 105^\circ \).

Answer:

\( m\angle YXZ = 105^\circ \)