Dominic goes jogging every morning. If m represents the number of miles he jogs each day, which expression represents the total
1 answer:
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<span>In triangle WXZ,
Line WY is an altitude (as shown in the attached picture)
Now, it is given that:
</span><span>If ΔYWZ ~ ΔYXW
</span>∠WXY = ∠WZY
<span>
Then, we can also conclude
</span>∠WYX = ∠WYZ = 90°....(1) (because WY is the altitude)
Now, in any triangle, the sum of all the three angles is 180.
In triangle, WXY, ∠WYX = 90° (From 1)
Therefore, WXY + XWY = 90°
Similarly, in WZY.
Hence, we conclude that XWZ is a right angle.
Line WY is an altitude (as shown in the attached picture)
Now, it is given that:
</span><span>If ΔYWZ ~ ΔYXW
</span>∠WXY = ∠WZY
<span>
Then, we can also conclude
</span>∠WYX = ∠WYZ = 90°....(1) (because WY is the altitude)
Now, in any triangle, the sum of all the three angles is 180.
In triangle, WXY, ∠WYX = 90° (From 1)
Therefore, WXY + XWY = 90°
Similarly, in WZY.
Hence, we conclude that XWZ is a right angle.
<span>The complete question is shown in the attached image
<u><em>Answer:</em></u>
measure angle H = 42</span>°<span>
<u><em>Explanation:</em></u>
<u>There is a theorem that states that:</u>
"In a triangle, the measure of the exterior angle is equal to the sum of the measures of the two non-adjacent angles to the exterior angle"
<u>In the given, we have:</u>
angle E is an exterior angle to triangle DFH
The two non-adjacent angles to angle E are angles D and H
<u>Based on the above rule:</u>
measure angle E = measure angle D + measure angle H
<u>We are given that:</u>
angle E = 87</span>°<span>
angle D = 45</span>°<span>
<u>Substitute with the givens in the above rule and solve for the measure of angle H as follows:</u>
angle E = angle D + angle H
87</span>°<span> = 45</span>°<span> + measure angle H
measure angle H = 87</span>°<span> - 45</span>°<span>
measure angle H = 42</span>°<span>
Hope this helps :)</span>
<u><em>Answer:</em></u>
measure angle H = 42</span>°<span>
<u><em>Explanation:</em></u>
<u>There is a theorem that states that:</u>
"In a triangle, the measure of the exterior angle is equal to the sum of the measures of the two non-adjacent angles to the exterior angle"
<u>In the given, we have:</u>
angle E is an exterior angle to triangle DFH
The two non-adjacent angles to angle E are angles D and H
<u>Based on the above rule:</u>
measure angle E = measure angle D + measure angle H
<u>We are given that:</u>
angle E = 87</span>°<span>
angle D = 45</span>°<span>
<u>Substitute with the givens in the above rule and solve for the measure of angle H as follows:</u>
angle E = angle D + angle H
87</span>°<span> = 45</span>°<span> + measure angle H
measure angle H = 87</span>°<span> - 45</span>°<span>
measure angle H = 42</span>°<span>
Hope this helps :)</span>