Question

part 2
find the measure of
each numbered angle.

1. $\angle 1$
2. $\angle 2$
3. $\angle 3$
4. houses the roof support on lamar’s house is in the shape

of an isosceles triangle with base angles of $38^\circ$. find $x$.
5.
find the measure of
each numbered angle.
$m\angle 1 = $ $m\angle 2 = $

Explanation:

Step1: Calculate $\angle 1$ (triangle sum)

The sum of angles in a triangle is $180^\circ$.
$m\angle 1 = 180^\circ - 75^\circ - 35^\circ = 70^\circ$

Step2: Calculate $\angle 2$ (supplementary to $\angle 1$)

$\angle 1$ and $\angle 2$ are a linear pair.
$m\angle 2 = 180^\circ - 70^\circ = 110^\circ$

Step3: Calculate $\angle 3$ (triangle sum)

Use the triangle with $\angle 2$ and $28^\circ$.
$m\angle 3 = 180^\circ - 110^\circ - 28^\circ = 42^\circ$

Step4: Calculate $x$ (isosceles triangle sum)

Sum of angles in a triangle is $180^\circ$.
$x = 180^\circ - 38^\circ - 38^\circ = 104^\circ$

Step5: Calculate $m\angle 2$ (right triangle angle)

$\angle Q$ is a right angle.
$m\angle 2 = 90^\circ - 51^\circ = 39^\circ$

Step6: Calculate $m\angle 1$ (exterior angle theorem)

$\angle 1$ is exterior to $\triangle QSR$.
$m\angle 1 = 39^\circ + 33^\circ = 72^\circ$

Answer:

1. $m\angle 1 = 70^\circ$
2. $m\angle 2 = 110^\circ$
3. $m\angle 3 = 42^\circ$
4. $x = 104^\circ$
5. $m\angle 1 = 72^\circ$, $m\angle 2 = 39^\circ$