Question

drag and drop your answers into the boxes to complete the explanation. in the figure \boxed{} and $angle 1$ are alternate interior angles. therefore, $mangle 1 = \boxed{}$ $angle 2$and $angle 5$ are alternate interior angles, so $mangle 2 = \boxed{}$ and $mangle 5 = \boxed{}$ also, $mangle 3 + mangle 4 + mangle 5 = 180^circ$, so $mangle 3 = \boxed{}$ so, $mangle 1 + mangle 2 + mangle 3 = \boxed{}$ 180° 58° 52° 70° $angle dba$ $angle dbg$ $angle 2$ $angle 4$

Explanation:

Step1: Identify alternate interior angle for ∠1

∠4 and ∠1 are alternate interior angles.

Step2: Set ∠1 equal to its alternate angle

Since alternate interior angles are congruent, $m\angle1 = m\angle4 = 70^\circ$

Step3: Match ∠2 to its alternate angle

∠2 and ∠5 are alternate interior angles, so $m\angle2 = m\angle5 = 52^\circ$

Step4: Calculate m∠3 using straight angle

Use $m\angle3 + m\angle4 + m\angle5 = 180^\circ$. Substitute known values:
$m\angle3 = 180^\circ - 70^\circ - 52^\circ = 58^\circ$

Step5: Sum the three triangle angles

$m\angle1 + m\angle2 + m\angle3 = 70^\circ + 52^\circ + 58^\circ = 180^\circ$

Answer:

In the figure $\boldsymbol{\angle4}$ and $\angle1$ are alternate interior angles. Therefore, $m\angle1 = \boldsymbol{70^\circ}$. $\angle2$ and $\angle5$ are alternate interior angles, so $m\angle2 = \boldsymbol{52^\circ}$ and $m\angle5 = \boldsymbol{52^\circ}$. Also, $m\angle3 + m\angle4 + m\angle5 = 180^\circ$, so $m\angle3 = \boldsymbol{58^\circ}$. So, $m\angle1 + m\angle2 + m\angle3 = \boldsymbol{180^\circ}$