Question

In the given picture, the measure of x is __°

*no multiple choice*
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Answer 1

Let us assume that,

→ x + y + 90° = 180°

Now the required value of y is,

→ y + 142° = 180°

→ y = 180° - 142°

→ [ y = 38° ]

Then the value of x will be,

→ x + 38° + 90° = 180°

→ x = 180° - 128°

→ [ x = 52° ]

Hence, the value of x is 52°.

Answer 2

x = 52°

Explanation:

Exterior Angle Theorem

The interior angles of a triangle sum to 180°. Angles on a straight line sum to 180°. Therefore, the exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles of the triangle.

⇒ x + 90° = 142°

⇒ x + 90° - 90° = 142° - 90°

⇒ x = 52°