Question

find the missing angle.
(left triangle: angle at d with exterior angle 100°, angle at f is 65°, find angle at e; right triangle: right - angled, one angle 35°, find the other non - right angle)

Explanation:

Left Triangle (∠D = 100°? Wait, no, the angle at D with the line R is 100°, so the interior angle at D is supplementary to 100°? Wait, no, let's correct. The angle adjacent to 100° (on a straight line) is 180° - 100° = 80°. Then, in triangle DEF, we have angles: at D (interior) is 80°, at F is 65°, so the missing angle at E is 180° - 80° - 65°. Wait, maybe I misread. Wait, the left figure: angle at D with the external line is 100°, so the internal angle at D is 180° - 100° = 80°. Then triangle has angles 80°, 65°, so the third angle (at E) is 180 - 80 - 65 = 35°? Wait, no, let's do step by step.

Left Triangle (Finding ∠E):

Step1: Find interior angle at D.

The angle adjacent to 100° (linear pair) is $180^\circ - 100^\circ = 80^\circ$.

Step2: Sum of angles in a triangle.

Sum of angles in a triangle is $180^\circ$. So, ∠E = $180^\circ - 80^\circ - 65^\circ$.

Step3: Calculate ∠E.

$180 - 80 - 65 = 35^\circ$.

Right Triangle (Finding the missing angle, right triangle, so one angle is 90°):

Step1: Sum of angles in right triangle.

In a right triangle, one angle is $90^\circ$, sum of angles is $180^\circ$. So, missing angle = $180^\circ - 90^\circ - 35^\circ$.

Step2: Calculate missing angle.

$180 - 90 - 35 = 55^\circ$.

Answer:

s:
Left triangle missing angle (∠E): $35^\circ$
Right triangle missing angle: $55^\circ$