Question

48.
triangle image with two equal sides marked and two base angles marked
name this triangle.
a) equilateral, obtuse b) isosceles, acute
c) right, isosceles d) scalene, acute
49.
triangle image with angles 45° and 88° marked, and one angle ?
a) 133 b) 57
c) 47 d) 53

Explanation:

Question 48

Step1: Identify triangle type by sides

The triangle has two equal - length sides (marked with tick marks), so it is isosceles (equilateral has all three equal, scalene has all different).

Step2: Identify triangle type by angles

The sum of angles in a triangle is \(180^{\circ}\). Let the base angles be equal (since it's isosceles). Let each base angle be \(x\), and the vertex angle be \(y\). We know that the two base angles are equal. From the diagram, we can see that the angles are all less than \(90^{\circ}\) (since it's a triangle with two equal sides and the vertex angle is acute). So it is an acute triangle (obtuse has one angle \(> 90^{\circ}\), right has one angle \( = 90^{\circ}\)).

Step1: Recall angle - sum property

The sum of the interior angles of a triangle is \(180^{\circ}\). Let the unknown angle be \(x\).

Step2: Set up the equation

We know two angles: \(45^{\circ}\) and \(88^{\circ}\). So, \(x+45^{\circ}+88^{\circ}=180^{\circ}\).

Step3: Solve for \(x\)

First, add \(45^{\circ}\) and \(88^{\circ}\): \(45 + 88=133\). Then, \(x=180 - 133\). So, \(x = 47^{\circ}\).

Answer:

b) Isosceles, acute

Question 49