Question

1. find the measure of < h

Explanation:

Step1: Find base angles of large triangle

First, calculate the two unknown base angles of the large outer triangle.
For the left base angle: $180^\circ - 30^\circ = 150^\circ$ (linear pair), so the inner base angle is $180^\circ - 70^\circ - 150^\circ$ is incorrect. Correct: The sum of angles in a triangle is $180^\circ$. Let the left base angle of the large triangle be $\alpha$, right base angle be $\beta$.
$\alpha = 180^\circ - 70^\circ - \beta$, but better: The angles adjacent to $30^\circ$ and $25^\circ$ are the other two angles of the large triangle. Wait, no: The large triangle has top angle $70^\circ$, left base angle = $180^\circ - 30^\circ - x$? No, correct step:

Step1: Calculate large triangle base angles

Sum of angles in triangle is $180^\circ$.
Left base angle of large triangle: $180^\circ - 70^\circ - (180^\circ - 25^\circ)$ is wrong. Correct: The two base angles of the large triangle are:
Left base angle: let it be $A$, right base angle be $B$.
$A = 180^\circ - 30^\circ - \text{angle adjacent to } h$? No, better:

Step1: Find missing angles of small triangles

The large triangle has angles $70^\circ$, $(30^\circ + x)$, $(25^\circ + y)$, where $x$ and $y$ are the other two angles of the inner triangle with $\angle h$.
Sum of angles in large triangle: $70^\circ + (30^\circ + x) + (25^\circ + y) = 180^\circ$
$125^\circ + x + y = 180^\circ$
$x + y = 55^\circ$

Step2: Calculate $\angle h$

Sum of angles in inner triangle is $180^\circ$.
$\angle h = 180^\circ - (x + y)$
$\angle h = 180^\circ - 55^\circ = 125^\circ$

Answer:

$125^\circ$