Question

question 18 7 pts find the measure of the missing angles. m∠1 = m∠2 = m∠3 = m∠4 = m∠5 = m∠6 = m∠7 =

Explanation:

Step1: Identify perpendicular lines

Lines $t$ and $a$ are perpendicular, so $\angle1 = 90^{\circ}$.

Step2: Vertical - angle property

$\angle1$ and $\angle3$ are vertical angles, so $m\angle3=m\angle1 = 90^{\circ}$.

Step3: Linear - pair property

$\angle1$ and $\angle2$ form a linear pair. Since $\angle1 = 90^{\circ}$, then $m\angle2=180 - 90=90^{\circ}$.

Step4: Corresponding - angle property

Lines $a$ and $b$ are parallel (implied by the similar perpendicular - line structure). $\angle1$ and $\angle4$ are corresponding angles, so $m\angle4 = 90^{\circ}$.

Step5: Vertical - angle property

$\angle4$ and $\angle6$ are vertical angles, so $m\angle6=m\angle4 = 90^{\circ}$.

Step6: Linear - pair property

$\angle4$ and $\angle5$ form a linear pair. Since $\angle4 = 90^{\circ}$, then $m\angle5=180 - 90 = 90^{\circ}$.

Step7: Vertical - angle property

$\angle5$ and $\angle7$ are vertical angles, so $m\angle7=m\angle5 = 90^{\circ}$.

Answer:

$m\angle1 = 90^{\circ}$
$m\angle2 = 90^{\circ}$
$m\angle3 = 90^{\circ}$
$m\angle4 = 90^{\circ}$
$m\angle5 = 90^{\circ}$
$m\angle6 = 90^{\circ}$
$m\angle7 = 90^{\circ}$