ABC is a right-angled triangle in which ∠A = 90° and AB = AC. Find ∠B and ∠C.

Solution:

We can use the property that angles opposite to equal sides are equal and then by using angle sum property in triangle ABC we can find the value of ∠B and ∠C.

It is given that,

AB = AC

∴ ∠C = ∠B (Angles opposite to equal sides are also equal)

Let ∠B = ∠C = x

In ΔABC,

∠A + ∠B + ∠C = 180° (Angle sum property of a triangle)

90°+ x + x = 180°

90°+ 2x = 180°

2x = 90°

x = 45°

∴ ∠B = ∠C = 45°

☛ Check: NCERT Solutions for Class 9 Maths Chapter 7

Video Solution:

ABC is a right-angled triangle in which ∠A = 90° and AB = AC. Find ∠B and ∠C.

NCERT Maths Solutions Class 9 Chapter 7 Exercise 7.2 Question 7

Summary:

If ABC is a right-angled triangle in which ∠A = 90° and AB = AC, then the value of ∠B and ∠C are equal to 45°(∠B = ∠C = 45°)

☛ Related Questions:

• ABC is an isosceles triangle in which altitudes BE and CF are drawn to equal sides AC and AB respectively (see Fig. 7.31). Show that these altitudes are equal.
• ABC is a triangle in which altitudes BE and CF to sides AC and AB are equal (see Fig. 7.32). Show that(i) ΔABE ≅ ΔACF(ii) AB = AC, i.e., ABC is an isosceles triangle.
• ABC and DBC are two isosceles triangles on the same base BC (see Fig. 7.33). Show that ∠ABD = ∠ACD.
• ΔABC is an isosceles triangle in which AB = AC. Side BA is produced to D such that AD = AB (see Fig. 7.34). Show that ∠BCD is a right angle.