Question

Find the values of m and n.

Answer 1

Answer:

$m=46^{\circ},\\n=22^{\circ}$

Step-by-step explanation:

From the isosceles-base theorem, the base angles of two equal legs in a triangle must be equal. Thus, we can set the up the following equation to solve for $n$:

$136+n+n=180,\\136+2n=180,\\2n=44,\\n=\boxed{22^{\circ}}$

Now that we've found $n$, we can set up the following equation with respect to the largest triangle:

$90+n+m+n=180,\\90+22+m+22=180,\\134+m=180,\\m=\boxed{46^{\circ}}$

Answer 2

Answer:

M = 46°

N = 22°

Step-by-step explanation:

Value of M:

Sum of angles in triangle = 180°

180° - 90° - (180° - 136°) = m

90° - 44° = m

m = 46°

Value of N:

The triangle is isosceles (marked by the two congruent lines with the tick)

That means that the other two angles, are the same

180° - 136° = 2n

44° = 2n

n = 22°

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-Chetan K