In the diagram below, BD is parallel to XY. What is the value of y?
2 answers:
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Answer:
The measure of the first angle is 50°.
Step-by-step explanation:
Let the three angles be <em>a, b, </em>and <em>c. </em>
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The measure of the first angle is twice the measure of the second angle. In other words:
The measure of the third angle is 80° more than the measure of the second angle. In other words:
And since the interior angles of a triangle must equal 180°:
Substitute <em>a</em> and <em>c: </em>
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Combine like terms:
Subtract 80 from both sides:
And divide both sides by four:
So, the measure of the second angle is 25°.
Since the measure of the first is twice the second, the measure of the first angle is 50°.
(And since the measure of the third is 80° than the second, the measure of the third angle is 105°.)