Question

find the value of x then classify the triangle.
1.
2.
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11.
14.

Explanation:

Problem 1:

Step1: Sum of angles in triangle is \(180^\circ\).

\(45^\circ + 44^\circ + x^\circ = 180^\circ\)

Step2: Calculate \(x\).

\(89^\circ + x^\circ = 180^\circ\)
\(x = 180 - 89 = 91\)
Since one angle is \(91^\circ\) (obtuse), triangle is obtuse scalene.

Step1: Sum of angles in triangle is \(180^\circ\). Let the first angle be \(y\) (but we know two angles: \(y\) and \(27^\circ\), wait, the diagram shows two angles? Wait, maybe it's a typo, but assuming two angles: let's say the first angle is \(y\), but maybe it's an isosceles? Wait, no, the problem says "Find \(x\)". Wait, maybe the triangle has angles \(x\), \(x\), and \(27^\circ\)? Wait, no, the diagram: first triangle (problem 2) has two angles? Wait, maybe the user made a typo, but assuming it's a triangle with angles \(x\), \(x\), and \(27^\circ\) (isosceles). Wait, no, sum of angles: \(x + x + 27 = 180\)

Step2: Solve for \(x\).

\(2x = 180 - 27 = 153\)
\(x = \frac{153}{2} = 76.5\)
Triangle is isosceles (two angles equal) and acute (all angles \(< 90^\circ\)).

Step1: Sum of angles in triangle is \(180^\circ\).

\(53^\circ + 37^\circ + x^\circ = 180^\circ\)

Step2: Calculate \(x\).

\(90^\circ + x^\circ = 180^\circ\)
\(x = 90\)
Triangle is right (one angle \(90^\circ\)) and scalene (all sides different, angles \(53, 37, 90\)).

Answer:

\(x = 91\), Obtuse Scalene Triangle

Problem 2: