Question

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

∠6 is a right angle

∠a + ∠b = 90°

Explanation:

Step1: Identify vertical - angle relationship

$\angle3$ and $\angle6$ are vertical angles. Since $\angle6$ is a right - angle ($90^{\circ}$), then $\angle3 = 90^{\circ}$ (Vertical angles are equal).

Step2: Use linear - pair property

$\angle a+\angle b+\angle3=180^{\circ}$ because they form a linear pair.

Step3: Substitute the value of $\angle3$

Substitute $\angle3 = 90^{\circ}$ into $\angle a+\angle b+\angle3 = 180^{\circ}$. We get $\angle a+\angle b+90^{\circ}=180^{\circ}$.

Step4: Solve for $\angle a+\angle b$

Subtract $90^{\circ}$ from both sides of the equation $\angle a+\angle b+90^{\circ}=180^{\circ}$. So, $\angle a+\angle b=180^{\circ}-90^{\circ}=90^{\circ}$.

Answer:

The proof is completed as shown above. $\angle a+\angle b = 90^{\circ}$ is proved.