In Fig. 6.45, if ST = SU, then find the values of x and y.
Solution:
Given, STU is a triangle.
Also, ST = SU
We have to find the values of x and y.
We know that the vertically opposite angles are equal.
From the figure,
∠TSU = 78°
We know that the angles opposite to the equal sides are equal.
Now, ∠T = ∠U = y
Considering triangle STU,
Angle sum property of a triangle states that the sum of all three interior angles of a triangle is always equal to 180 degrees.
∠S + ∠T + ∠U = 180°
78° + y + y = 180°
78° + 2y = 180°
2y = 180° - 78°
2y = 102°
y = 102°/2
y = 51°
We know that the sum of a linear pair of angles is equal to 180 degrees.
So, x + y = 180°
x + 51° = 180°
x = 180° - 51°
x = 129°
Therefore, the values of x and y are 129° and 51°.
✦ Try This: In the given figure, ∠A = 50°, CE ∥ BA and ∠ECD = 60°. Then, ∠ACB = ?
☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 6
NCERT Exemplar Class 7 Maths Chapter 6 Problem 137
In Fig. 6.45, if ST = SU, then find the values of x and y.
Summary:
In Fig. 6.45, if ST = SU, then the values of x and y are 129° and 51°.
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