Question

Help meeee please i struggle ​

Answer 1

m∠M=28°

Step-by-step explanation:

In the given figure we can see that the exterior angle at P is 48°.

From the axiom that when a line intersect other line, the angles formed have a sum of 180°

So the interior angle at P will be: 180°-48° = 132°

Now let

m∠P = 132°

m∠M = (3y+1)°

m∠N= (2y+2)°

As the sum of internal angles of triangle is 180°

So,

$M+N+P = 180\\3y+1+2y+2+132=180\\5y+135=180$

Subtracting 135 from both sides

$5y+135-135=180-135\\5y=45$

Dividing both sides by 5

$\frac{5y}{5}=\frac{45}{5}\\y=9$

So,

m∠M = 3y+1 = 3(9)+1 = 27+1 = 28°

Hence,

m∠M=28°

Keywords: Triangle, Geometry

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