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Find the size of the third angle in each triangle. The total sum of a triangle is 180°

Mathematics

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Answers

2 parts
a

Q=130∘Q = 130^\circ

b

θ=55∘\theta = 55^\circ

Step-by-step solution

4 steps

Here's how to find the size of the third angle in each triangle:

The sum of the angles in any triangle is 180∘180^\circ.

Part a· 2 steps

For the first triangle

  1. Add the two given angles.

    26∘+24∘=50∘26^\circ + 24^\circ = 50^\circ
  2. Subtract this sum from 180∘180^\circ to find the third angle, QQ.

    Q=180∘−50∘Q = 180^\circ - 50^\circ Q=130∘Q = 130^\circ

    The third angle is Q=130∘\boxed{Q = 130^\circ}.

Part b

θ=55∘\theta = 55^\circ

For the second triangle

  1. Add the two given angles.

    Note that the square symbol indicates a right angle, which is 90∘90^\circ.

    90∘+35∘=125∘90^\circ + 35^\circ = 125^\circ
  2. Subtract this sum from 180∘180^\circ to find the third angle, θ\theta.

    θ=180∘−125∘\theta = 180^\circ - 125^\circ θ=55∘\theta = 55^\circ

    The third angle is θ=55∘\boxed{\theta = 55^\circ}.

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