Question

find the missing angle.
? 60° 80°
find the missing angle.
d? e 75° k c 45°

Explanation:

Step1: Sum of triangle angles is $180^\circ$

Let missing angle be $x$.
$x + 60^\circ + 80^\circ = 180^\circ$

Step2: Calculate left-side sum

$x + 140^\circ = 180^\circ$

Step3: Solve for first missing angle

$x = 180^\circ - 140^\circ = 40^\circ$

Step4: Find $\angle CED$ (supplementary angle)

$\angle CED = 180^\circ - 75^\circ = 105^\circ$

Step5: Sum of angles in $\triangle CDE$

Let missing angle be $y$.
$y + 45^\circ + 105^\circ = 180^\circ$

Step6: Calculate left-side sum

$y + 150^\circ = 180^\circ$

Step7: Solve for second missing angle

$y = 180^\circ - 150^\circ = 30^\circ$

Answer:

First triangle missing angle: $40^\circ$
Second triangle missing angle: $30^\circ$