Question

solve for x
a) -10
c) -8
b) -12
d) -5

solve for x
a) 85°
c) 45°
b) -88
d) -7°

44 match the following triangles with their correct definition:

• all sides are the same length.
• has at least 2 equal sides.
• has no equal sides.
• has one right angle.
• has 3 acute angles.

45 what kind of triangle is this? (triangle with angles 35°, 51°, 94°? wait, no, 35°, 50°, 95°? wait, the blue triangle has angles 35°, 50°, and 95°? wait, no, the labels: 35°, 51°, 50°? wait, the options are a) obtuse, b) acute, c) right

Explanation:

Step1: Recall triangle angle sum

The sum of angles in a triangle is \(180^\circ\). So, \(70^\circ + 65^\circ + (x + 53)^\circ = 180^\circ\).

Step2: Simplify the equation

First, add \(70\) and \(65\): \(70 + 65 = 135\). Then the equation becomes \(135 + x + 53 = 180\). Combine like terms: \(x + 188 = 180\).

Step3: Solve for x

Subtract \(188\) from both sides: \(x = 180 - 188 = -8\)? Wait, no, wait. Wait, \(70 + 65 + x + 53 = 180\). Wait, \(70 + 65 = 135\), \(135 + 53 = 188\). So \(x + 188 = 180\)? That would give \(x = -8\), but let's check again. Wait, maybe I misread the angle. Wait, the triangle has angles \(70^\circ\), \(65^\circ\), and \(x + 53\). So sum is \(70 + 65 + x + 53 = 180\). So \(188 + x = 180\), so \(x = -8\)? But let's check the options. Option c is -8. Wait, but maybe I made a mistake. Wait, no, the sum of angles in a triangle is \(180\). So \(70 + 65 = 135\), \(180 - 135 = 45\). Wait, no! Wait, \(x + 53\) is the third angle. So \(70 + 65 + (x + 53) = 180\). So \(x + 53 = 180 - 70 - 65 = 45\). Then \(x = 45 - 53 = -8\). Yes, that's correct. So x is -8.

For the triangle type question: The angles are \(35^\circ\), \(50^\circ\), and \(95^\circ\)? Wait, no, \(35 + 50 + 95 = 180\)? Wait, \(35 + 50 = 85\), \(180 - 85 = 95\). Wait, no, the triangle has angles \(35^\circ\), \(50^\circ\), and let's calculate the third angle: \(180 - 35 - 50 = 95^\circ\). Wait, but the options are a) obtuse, b) acute, c) right. An obtuse triangle has one angle greater than \(90^\circ\). \(95^\circ\) is greater than \(90^\circ\), so it's obtuse? Wait, no, wait the angles given are \(35^\circ\), \(50^\circ\), and let's check again. Wait, the triangle in the image (the blue one) has angles \(35^\circ\), \(50^\circ\), and the third angle: \(180 - 35 - 50 = 95^\circ\). So one angle is obtuse (greater than \(90^\circ\)), so the triangle is obtuse? But the options are a) obtuse, b) acute, c) right. So answer a) obtuse? Wait, but let's check the options again. Wait, the question is "What kind of triangle is this?" with angles \(35^\circ\), \(50^\circ\), and \(95^\circ\) (since \(35 + 50 + 95 = 180\)). So since one angle is greater than \(90^\circ\) (obtuse), the triangle is obtuse. So option a) obtuse.

Answer:

For the first problem (solve for x in the triangle with angles \(70^\circ\), \(65^\circ\), \(x + 53\)): \(\boxed{-8}\) (corresponding to option c).

For the triangle type problem: The triangle is obtuse, so the answer is a) obtuse.