Question

given: m || n
∠6 is a right angle
prove: ∠a + ∠b = 90°
statements reasons
given
∠6 is a right angle
∠a + ∠b = 90°

Explanation:

Step1: State given facts

$m\parallel n$ and $\angle6 = 90^{\circ}$ (Given)

Step2: Use corresponding - angles property

Since $m\parallel n$, $\angle2=\angle6$ (Corresponding angles of parallel lines are equal). So $\angle2 = 90^{\circ}$ (Substitution property of equality)

Step3: Use linear - pair property

$\angle1+\angle2 = 180^{\circ}$ (Linear - pair postulate). Since $\angle2 = 90^{\circ}$, then $\angle1=90^{\circ}$ (Subtraction property of equality)

Step4: Use angle - addition postulate

$\angle1=\angle a+\angle b$ (Angle - addition postulate). Since $\angle1 = 90^{\circ}$, then $\angle a+\angle b = 90^{\circ}$ (Substitution property of equality)

Answer:

Statements	Reasons
$\angle6$ is a right angle	Given
$\angle2=\angle6$	Corresponding angles of parallel lines are equal
$\angle2 = 90^{\circ}$	Substitution property of equality
$\angle1+\angle2 = 180^{\circ}$	Linear - pair postulate
$\angle1 = 90^{\circ}$	Subtraction property of equality
$\angle1=\angle a+\angle b$	Angle - addition postulate
$\angle a+\angle b = 90^{\circ}$	Substitution property of equality