Using Properties of Parallel Lines

We can start by determining $u$ using the Corresponding Angles Theorem.

We are given the measure of

5 3^{\circ}

for one of the angles. Since this is a corresponding angle to

u^{\circ},

they are congruent.

u = 53

Next,

u^{\circ}

and

w^{\circ}

are a linear pair and, thus, the sum of their measure is

18 0^{\circ} .

Therefore, we can write the following equation.

u^{\circ} + w^{\circ} = 18 0^{\circ}

Since we know

u

we can find

w .

u^{\circ} + w^{\circ} = 18 0^{\circ}

u = 53

53^{\circ} + w^{\circ} = 18 0^{\circ}

LHS - 53 = RHS - 53

w^{\circ} = 12 7^{\circ}

The value of

w

is

127 .

Using Properties of Parallel Lines 1.8 - Solution