Answer
$m \angle 1 = 90^{\circ}$
$m \angle 2 = 55^{\circ}$
$m \angle 3 = 90^{\circ}$
Work Step by Step
Diagonals of rhombuses cross each other at right angles, so $m \angle 1 = m\angle 3 = 90^{\circ}$.
Let's look at one of the smaller triangles. We have one angle measuring $90^{\circ}$ and an angle that measures $35^{\circ}$; therefore, we only have to find the measure of one more angle.
The interior angles of a triangle add up to $180^{\circ}$, so let's set up an equation where we can find the measure of one of the interior angles given the measures of the other two angles:
$m$ third angle = $180 - (90 + 35)$
Evaluate parentheses first, according to order of operations:
$m$ third angle = $180 - (125)$
Subtract to solve:
$m$ third angle = $55$
If we know the measure of this angle, then we also know $m \angle 2$ because the larger angle that these two angles are parts of are both bisected by the same diagonal. Therefore, $m \angle 2 = 55^{\circ}$.
